Graphic summary
  • Show / hide key
  • Information


Scientific and technological production
  •  

1 to 50 of 91 results
  • Corrigendum to "Algebraic characterizations of regularity properties in bipartite graphs" Eur. J. Combin. 34 (2013) 1223-1231

     Abiad, Aida; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    European journal of combinatorics
    Date of publication: 2014
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    Corrigendum d'un article anteriorment publicat

    Postprint (author’s final draft)

  • The (Delta,D) and (Delta,N) problems in double-step digraphs with unilateral distance

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Electronic Journal of Graph Theory and Applications
    Date of publication: 2014
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    We study the (;D) and (;N) problems for double-step digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse digraph, the latter obtained by changing the directions of all the arcs. The first problem consists of maximizing the number of vertices N of a digraph, given the maximum degree and the unilateral diameter D, whereas the second one (somehow dual of the first) consists of minimizing the unilateral diameter given the maximum degree and the number of vertices. We solve the first problem for every value of the unilateral diameter and the second one for infinitely many values of the number of vertices. Moreover, we compute the mean unilateral distance of the digraphs in the families considered.

    We study the (delta;D) and (delta;N) problems for double-step digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse digraph, the latter obtained by changing the directions of all the arcs. The first problem consists of maximizing the number of vertices N of a digraph, given the maximum degree and the unilateral diameter D , whereas the second one (somehow dual of the first) consists of minimizing the unilateral diameter given the maximum degree and the number of vertices. We solve the first problem for every value of the unilateral diameter and the second one for infinitely many values of the number of vertices. Moreover, we compute the mean unilateral distance of the digraphs in the families considered.

  • Edge-distance-regular graphs are distance-regular

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Delorme, Charles; Fiol Mora, Miquel Àngel; Suzuki, Hiroshi
    Journal of combinatorial theory. Series A
    Date of publication: 2013
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    Edge-distance-regular graph; Homogeneous graph; Bipartite distance-regular graph; Generalized odd graph; Orthogonal polynomials

    A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-regular or a generalized odd graph. Also, we obtain the relationships between some of their corresponding parameters, mainly, the distance polynomials and the intersection numbers.

  • The (¿,D) and (¿,N) problems for New Amsterdam and Manhattan digraphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    AKCE International Journal of Graphs and Combinatorics
    Date of publication: 2013-10
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    We give a quasi-complete solution of the (¿,N) problem for two well-known families of digraphs used as good models for large interconnection networks. In our study we also relate both families, the New Amsterdam and Manhattan digraphs, with the double-step graphs (or circulant graphs with degree two).

  • Algebraic Characterizations of Regularity Properties in Bipartite Graphs

     Abiad Monge, Aida; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    European journal of combinatorics
    Date of publication: 2013
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distance-regularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the Hoffman polynomial. Moreover, it is shown that the conditions for having distance-regularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.

    Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distance-regularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the Hoffman polynomial. Moreover, it is shown that the conditions for having distance-regularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.

  • Access to the full text
    The Manhattan product of digraphs  Open access

     Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Electronic Journal of Graph Theory and Applications
    Date of publication: 2013
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants.

  • Access to the full text
    Moments in graphs  Open access

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Discrete applied mathematics
    Date of publication: 2013
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    This parameter generalizes, or it is closely related to, some well-known graph invariants, such as the Wiener index W (G), when rho(u) = 1/2 for every u is an element of V, and the degree distance D'(G), obtained when rho(u) = delta(u), the degree of vertex u. In this paper we derive some exact formulas for computing the rho-moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding rho-moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same rho-moment for every rho (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product.

    Let G be a connected graph with vertex set V and a weight function that assigns a nonnegative number to each of its vertices. Then, the -moment of G at vertex u is de ned to be M G(u) = P v2V (v) dist(u; v), where dist( ; ) stands for the distance function. Adding up all these numbers, we obtain the -moment of G: This parameter generalizes, or it is closely related to, some well-known graph invari- ants, such as the Wiener index W(G), when (u) = 1=2 for every u 2 V , and the degree distance D0(G), obtained when (u) = (u), the degree of vertex u. In this paper we derive some exact formulas for computing the -moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding -moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same -moment for every (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product.

    Postprint (author’s final draft)

  • On some spectral and quasi-spectral characterizations of distance-regular graphs

     Abiad, Aida; Van Dam, Edwin R; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    GraphMasters Workshop
    Presentation's date: 2013-06-26
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • The (Delta,D) and (Delta,N) problems in double-steps digraphs with unilateral distance

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    GraphMasters Workshop
    Presentation's date: 2013-06-26
    Presentation of work at congresses

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    We study the (;D) and (;N) problems for double-step digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse digraph, obtained by changing the directions of all the arcs. The rst problem consists of maximizing the number of vertices N of a digraph, given the maximum degree and the unilateral diameter D, whereas the second one (somehow dual of the rst) consists of minimizing the unilateral diameter given the maximum degree and the number of vertices. We solve the rst problem for every value of the unilateral diameter and the second one for some innitely many values of the number of vertices. Moreover, we compute the mean unilateral distance of the digraphs in the families considered.

  • Access to the full text
    The (Delta,D) and (Delta,N) problems in double-step digraphs with unilateral diameter  Open access

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    European Conference on Combinatorics, Graph Theory and Applications
    Presentation's date: 2013-09-09
    Presentation of work at congresses

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We study the (D;D) and (D;N) problems for double-step digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse digraph, obtained by changing the directions of all the arcs. The first problem consists of maximizing the number of vertices N of a digraph, given the maximum degree D and the unilateral diameter D , whereas the second one consists of minimizing the unilateral diameter given the maximum degree and the number of vertices. We solve the first problem for every value of the unilateral diameter and the second one for some infinitely many values of the number of vertices. Miller and Sirán [4] wrote a comprehensive survey about (D;D) and (D;N) problems. In particular, for the double-step graphs considering the standard diameter, the first problem was solved by Fiol, Yebra, Alegre and Valero [3], whereas Bermond, Iliades and Peyrat [2], and also Beivide, Herrada, Balcázar and Arruabarrena [1] solved the (D;N) problem. In the case of the double-step digraphs, also with the standard diameter, Morillo, Fiol and Fàbrega [5] solved the (D;D) problem and provided some infinite families of digraphs which solve the (D;N) problem for their corresponding numbers of vertices

    Postprint (author’s final draft)

  • Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación

     Aguilo Gost, Francisco de Asis Luis; Abiad Monge, Aida; Andrés Yebra, José Luis; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Ball, Simeon Michael; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Espona Dones, Margarida; Sau Valls, Ignasi; Montejano Cantoral, Amanda; Perarnau Llobet, Guillem; Moragas Vilarnau, Jordi; Vena Cros, Lluís; Andres Yebra, Jose Luis; Fiol Mora, Miquel Àngel
    Participation in a competitive project

     Share

  • WORKSHOP ON GRAPH SPECTRA APPLICATIONS IN COMPUTER SCIENCE

     Fàbrega Canudas, Josep; Comellas Padro, Francesc de Paula; Mitjana Riera, Margarida; Stevanovic, Dragan; Dalfo Simo, Cristina
    Participation in a competitive project

     Share

  • New results on (Delta,D) and (Delta,N) problems for some double-step digraphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    International Workshop on Optimal Network Topologies
    Presentation's date: 2012-07-27
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Edge-distance regular graphs are distance regular

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Delorme, Charles; Fiol Mora, Miquel Àngel; Suzuki, Hiroshi
    ICTP-IPM Workshop and Conference in Combinatorics and Graph Theory
    Presentation's date: 2012-09-10
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Characterizing distance-regular graphs that are edge-distance-regular

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    ESF Research Conferences
    Presentation's date: 2012-06
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Dual concepts of almost distance-regularity and the spectral excess theorem

     Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Discrete mathematics
    Date of publication: 2011
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    A differential approach for bounding the index of graphs under perturbations  Open access

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Electronic journal of combinatorics
    Date of publication: 2011-09-02
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    This paper presents bounds for the variation of the spectral radius (G) of a graph G after some perturbations or local vertex/edge modifications of G. The perturbations considered here are the connection of a new vertex with, say, g vertices of G, the addition of a pendant edge (the previous case with g = 1) and the addition of an edge. The method proposed here is based on continuous perturbations and the study of their differential inequalities associated. Within rather economical information (namely, the degrees of the vertices involved in the perturbation), the best possible inequalities are obtained. In addition, the cases when equalities are attained are characterized. The asymptotic behavior of the bounds obtained is also discussed.

  • Access to the full text
    Edge distance-regular graphs  Open access

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Electronic notes in discrete mathematics
    Date of publication: 2011
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.

    * distance-regularity; * local spectra; * predistance polynomials; * the spectral excess theorem; * generalized odd graphs

  • Edge-distance-regular graphs

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Journal of combinatorial theory. Series A
    Date of publication: 2011
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.

  • On perturbations of almost distance-regular graphs

     Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel
    Linear algebra and its applications
    Date of publication: 2011
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    A differential approach for bounding the index of graphs under perturbations  Open access

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Date: 2011-03
    Report

    Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    Edge-distance-regular graphs  Open access

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Date: 2011-03-11
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edgedistance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.

  • Edge-distance-regularity

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    International Workshop on Network Topologies
    Presentation's date: 2011-07-14
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • A new differencial approach to bound the spectral radius of graphs under perturbations

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Slovenian International Conference on Graph Theory
    Presentation's date: 2011-06-21
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Edge-distance-regular graphs

     Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    European Conference on Combinatorics, Graph Theory and Applications
    Presentation's date: 2011-08-31
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Access to the full text
    Graphs, Friends and Acquaintances  Open access

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Date: 2010-04-23
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    As is well known, a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Therefore, it is not surprising that many of the first results concerning graphs made reference to relationships between people or groups of people. In this article, we comment on four results of this kind, which are related to various general theories on graphs and their applications: the Handshake lemma (related to graph colorings and Boolean algebra), a lemma on known and unknown people at a cocktail party (to Ramsey theory), a theorem on friends in common (to distanceregularity and coding theory), and Hall’s Marriage theorem (to the theory of networks). These four areas of graph theory, often with problems which are easy to state but difficult to solve, are extensively developed and currently give rise to much research work. As examples of representative problems and results of these areas, which are discussed in this paper, we may cite the following: the Four Colors Theorem (4CTC), the Ramsey numbers, problems of the existence of distance-regular graphs and completely regular codes, and finally the study of topological proprieties of interconnection networks.

  • On almost distance-regular graphs

     Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
    Journal of combinatorial theory. Series A
    Date of publication: 2010
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distanceregular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. For example, a known characterization of a distance-regular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walk-regular if the number of closed walks of given length rooted at any given vertex is a constant. One of the concepts studied here is a generalization of both distance-regularity and walk-regularity called m-walkregularity. Another studied concept is that of m-partial distanceregularity or, informally, distance-regularity up to distance m. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distance-regularity, such as their common generalization of ( ,m)-walk-regularity. We introduce the concepts of punctual distance-regularity and punctual walk-regularity as a fundament upon which almost distanceregular graphs are built. We provide examples that are mostly taken from the Foster census, a collection of symmetric cubic graphs. Two problems are posed that are related to the question of when almost distance-regular becomes whole distance-regular. We also give several characterizations of punctually distance-regular graphs that are generalizations of the spectral excess theorem.

  • Characterizing (l, m)-walk-regular graphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Linear algebra and its applications
    Date of publication: 2010-12-30
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    Grafs, amics i coneguts  Open access

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Butlletí de la Societat Catalana de Matemàtiques
    Date of publication: 2010
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Com és ben sabut, un graf és un objecte matemàtic que modelitza l’existència d’una certa relació entre parells d’elements d’un conjunt donat. Aleshores, és natural que molts dels primers resultats sobre grafs facin referència a relacions entre persones o grups de persones. En aquest article, comentem quatre resultats d’aquest tipus, els quals tenen relació amb diverses teories generals de grafs i les seves aplicacions: el lema de les encaixades de mans (relacionat amb la coloració de grafs i l’àlgebra booleana), un lema sobre els coneguts i desconeguts en una festa (amb la teoria de Ramsey), un lema sobre els amics en comú (amb la distància-regularitat i la teoria de codis) i el teorema de les noces de Hall (amb la connectivitat de les xarxes). Aquestes quatre àrees de la teoria de grafs, amb problemes sovint fàcils de plantejar però molt difícils de resoldre, s’han desenvolupat extensament i actualment són motiu de nombrosos treballs de recerca. Com a exemples de resultats i problemes representatius d’aquestes àrees, els quals són motiu de discussió en aquest treball que presentem, podem citar els següents: el teorema dels quatre colors (T4C), els nombres de Ramsey, els problemes d’existència de grafs distància-regulars i de codis completament regulars i, finalment, l’estudi de les propietats topològiques de les xarxes d’interconnexió.

  • Characterizing (l,m)-walk-regular graphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga, Ernest
    Linear algebra and its applications
    Date of publication: 2010
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    The geometry of t-spreads in k-walk-regular graphs  Open access

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Journal of graph theory
    Date of publication: 2010-08
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    A graph is walk-regular if the number of closed walks of length rooted at a given vertex is a constant through all the vertices for all . For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D=d, we study the geometry of its d-spreads, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency matrix, we show that they form a simplex (or tetrahedron in a three-dimensional case) and we compute its parameters. Moreover, the results are generalized to the case of k-walk-regular graphs, a family which includes both walk-regular and distance-regular graphs, and their t-spreads or vertices at distance t from each other.

  • Access to the full text
    When almost distance-regularity attains distance-regularity  Open access

     Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    French Combinatorial Conference
    Presentation's date: 2010-06-28
    Presentation of work at congresses

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Generally speaking, `almost distance-regular graphs' are graphs which share some, but not necessarily all, regularity properties that characterize distance-regular graphs. In this paper we rst propose four basic di erent (but closely related) concepts of almost distance-regularity. In some cases, they coincide with concepts introduced before by other authors, such as walk-regular graphs and partially distance-regular graphs. Here it is always assumed that the diameter D of the graph attains its maximum possible value allowed by its number d+1 of di erent eigenvalues; that is, D = d, as happens in every distance-regular graph. Our study focuses on nding out when almost distance- regularity leads to distance-regularity. In other words, some `economic' (in the sense of minimizing the number of conditions) old and new characterizations of distance- regularity are discussed. For instance, if A0;A1; : : : ;AD and E0;E1; : : : ;Ed denote, respectively, the distance matrices and the idempotents of the graph; and D and A stand for their respective linear spans, any of the two following `dual' conditions su ce: (a) A0;A1;AD 2 A; (b) E0;E1;Ed 2 D. Moreover, other characterizations based on the preintersection parameters, the average intersection numbers and the recurrence coe cients are obtained. In some cases, our results can be also seen as a generalization of the so-called spectral excess theorem for distance-regular graphs.

  • Dual concepts of almost distance-regularity and the spectral excess theorem  Open access

     Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    International Workshop on Optimal Network Topologies
    Presentation of work at congresses

    Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

  • A taste of duality in almost distance-regularity

     Fiol Mora, Miquel Àngel; Dalfo Simo, Cristina; Van Dam, Edwin R; Garriga Valle, Ernest
    Swedish-Catalan Conference in Mathematics
    Presentation's date: 2010-09-17
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • When almost distance regularity attains distance regularity

     Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    International Workshop on Optimal Network Topologies
    Presentation's date: 2010-06-10
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • On almost distance-regular graphs

     Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
    Joint Mathematical Conference CSASC
    Presentation's date: 2010-01-25
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • On t-cliques in k-walk-regular graphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Electronic notes in discrete mathematics
    Date of publication: 2009-08
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    A graph is walk-regular if the number of cycles of length rooted at a given vertex is a constant through all the vertices. For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its d-cliques, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency matrix, we show that they form a regular tetrahedron and we compute its parameters. Moreover, the results are generalized to the case of k-walk-regular graphs, a family which includes both walk-regular and distance-regular graphs, and their t-cliques or vertices at distance t from each other.

  • COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

     Moragas Vilarnau, Jordi; Comellas Padro, Francesc de Paula; López Masip, Susana Clara; Mitjana Riera, Margarida; Llado Sanchez, Anna; Barriere Figueroa, Eulalia; Pérez Mansilla, Sonia; Zaragoza Monroig, Maria Luisa; Gomez Marti, Jose; Miralles De La Asuncion, Alicia; Garriga Valle, Ernest; Espona Dones, Margarida; Muñoz Lopez, Francisco Javier; Dalfo Simo, Cristina; Rius Font, Miquel; Aroca Farrerons, Josep Maria; Aguilo Gost, Francisco de Asis Luis; Cámara Vallejo, Marc; Gago Alvarez, Silvia; Ball, Simeon Michael; Andres Yebra, Jose Luis; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Pelayo Melero, Ignacio Manuel; Serra Albo, Oriol
    Participation in a competitive project

     Share

  • PROBLEMAS EXTREMALES Y DE OPTIMIZACIÓN EN TEORIA DE GRAFOS Y COMBINATORIA: APLICACIÓN AL ANALISIS Y ALGORITMOS DE REDES DE COMUNICAC

     Abiad Monge, Aida; Andres Yebra, Jose Luis; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Espona Dones, Margarida; Fàbrega Canudas, Josep; Gago Alvarez, Silvia; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Montejano Cantoral, Amanda; Moragas Vilarnau, Jordi; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Perarnau Llobet, Guillem; Pérez Mansilla, Sonia; Rius Font, Miquel; Sau Valls, Ignasi; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Vena Cros, Lluís; Fiol Mora, Miquel Àngel
    Participation in a competitive project

     Share

  • On t-cliques in k-walk-regular graphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    EUROCOMB'09: European Conference on Combinatorics, Graph Theory and Applicactions
    Presentation's date: 2009-09-10
    Presentation of work at congresses

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    A graph is walk-regular if the number of cycles of length rooted at a given vertex is a constant through all the vertices. For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its d-cliques, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency matrix, we show that they form a regular tetrahedron and we compute its parameters. Moreover, the results are generalized to the case of k-walk-regular graphs, a family which includes both walk-regular and distance-regular graphs, and their t-cliques or vertices at distance t from each other.

  • On k-walk-regular graphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    British Combinatorial Conference
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Les idees en didàctica de la matemàtica de Lluís Santaló

     Dalfo Simo, Cristina
    Date of publication: 2009-07
    Book chapter

     Share Reference managers Reference managers Open in new window

  • Fonaments matemàtics per a l'enginyeria de telecomunicació

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Gago Alvarez, Silvia; Heymann Pignolo, Marco; Tramuns Figueras, Eulalia
    Date of publication: 2009-07
    Book

     Share Reference managers Reference managers Open in new window

  • The hierarchical product of graphs

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Discrete applied mathematics
    Date of publication: 2009-01
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • On the hierarchical product of graphs and the generalized binomial tree

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Linear and multilinear algebra
    Date of publication: 2009
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • On k-Walk-Regular graphs

     Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Electronic journal of combinatorics
    Date of publication: 2009-04
    Journal article

     Share Reference managers Reference managers Open in new window

  • The generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Discrete mathematics
    Date of publication: 2009-06
    Journal article

     Share Reference managers Reference managers Open in new window

  • On middle cube graphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida; Dalfo Simo, Cristina; Barriere Figueroa, Eulalia
    SIAM Conference on Discrete Mathematics
    Presentation's date: 2008
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • A new operation on digraphs: the Manhattan product

     Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Jornadas de Matemática Discreta y Algorítmica
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window