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Corrigendum to "Algebraic characterizations of regularity properties in bipartite graphs" Eur. J. Combin. 34 (2013) 12231231
Abiad, Aida; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
European journal of combinatorics
Date of publication: 2014
Journal article
Read the abstract View Share Reference managersCorrigendum d'un article anteriorment publicat
Postprint (author’s final draft) 
The (Delta,D) and (Delta,N) problems in doublestep 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 View Share Reference managersWe study the (;D) and (;N) problems for doublestep 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 doublestep 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. 
Edgedistanceregular graphs are distanceregular
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 View Share Reference managersEdgedistanceregular graph; Homogeneous graph; Bipartite distanceregular graph; Generalized odd graph; Orthogonal polynomials
A graph is edgedistanceregular when it is distanceregular 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 edgedistanceregular graph Γ is distanceregular and homogeneous. More precisely, Γ is edgedistanceregular if and only if it is bipartite distanceregular 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: 201310
Journal article
Read the abstract View Share Reference managersWe give a quasicomplete solution of the (¿,N) problem for two wellknown 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 doublestep 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 View Share Reference managersRegular and distanceregular characterizations of general graphs are wellknown. In particular, the spectral excess theorem states that a connected graph GG is distanceregular 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 distanceregularity 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 distanceregularity 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 distanceregular characterizations of general graphs are wellknown. In particular, the spectral excess theorem states that a connected graph GG is distanceregular 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 distanceregularity 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 distanceregularity 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. 
The Manhattan product of digraphs
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 Access to the full text Share Reference managersWe 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. 
Moments in graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Discrete applied mathematics
Date of publication: 2013
Journal article
Read the abstract Access to the full text Share Reference managersThis parameter generalizes, or it is closely related to, some wellknown 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 rhomoment 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 rhomoments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same rhomoment 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 wellknown 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 quasispectral characterizations of distanceregular graphs
Abiad, Aida; Van Dam, Edwin R; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
GraphMasters Workshop
Presentation's date: 20130626
Presentation of work at congresses
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The (Delta,D) and (Delta,N) problems in doublesteps digraphs with unilateral distance
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
GraphMasters Workshop
Presentation's date: 20130626
Presentation of work at congresses
Read the abstract View Share Reference managersWe study the (;D) and (;N) problems for doublestep 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. 
The (Delta,D) and (Delta,N) problems in doublestep digraphs with unilateral diameter
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
European Conference on Combinatorics, Graph Theory and Applications
Presentation's date: 20130909
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersWe study the (D;D) and (D;N) problems for doublestep 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 doublestep 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 doublestep 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
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WORKSHOP ON GRAPH SPECTRA APPLICATIONS IN COMPUTER SCIENCE
Fàbrega Canudas, Josep; Comellas Padro, Francesc de Paula; Mitjana Riera, Margarida; Stevanovic, Dragan; Dalfo Simo, Cristina
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New results on (Delta,D) and (Delta,N) problems for some doublestep digraphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
International Workshop on Optimal Network Topologies
Presentation's date: 20120727
Presentation of work at congresses
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Edgedistance regular graphs are distance regular
Cámara Vallejo, Marc; Dalfo Simo, Cristina; Delorme, Charles; Fiol Mora, Miquel Àngel; Suzuki, Hiroshi
ICTPIPM Workshop and Conference in Combinatorics and Graph Theory
Presentation's date: 20120910
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Characterizing distanceregular graphs that are edgedistanceregular
Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
ESF Research Conferences
Presentation's date: 201206
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Dual concepts of almost distanceregularity 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
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A differential approach for bounding the index of graphs under perturbations
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic journal of combinatorics
Date of publication: 20110902
Journal article
Read the abstract Access to the full text Share Reference managersThis 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. 
Edge distanceregular graphs
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 Access to the full text Share Reference managersEdgedistanceregularity is a concept recently introduced by the authors which is similar to that of distanceregularity, 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 edgedistanceregular when it is distanceregular 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 edgedistanceregular if and only if its kincidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distanceregular graphs is proved, so giving a quasispectral characterization of edgedistanceregularity. Finally, it is shown that every nonbipartite graph which is both distanceregular and edgedistanceregular is a generalized odd graph.
* distanceregularity; * local spectra; * predistance polynomials; * the spectral excess theorem; * generalized odd graphs 
Edgedistanceregular 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 View Share Reference managersEdgedistanceregularity is a concept recently introduced by the authors which is similar to that of distanceregularity, 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 edgedistanceregular when it is distanceregular 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 edgedistanceregular if and only if its kincidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distanceregular graphs is proved, so giving a quasispectral characterization of edgedistanceregularity. Finally, it is shown that every nonbipartite graph which is both distanceregular and edgedistanceregular is a generalized odd graph. 
On perturbations of almost distanceregular graphs
Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel
Linear algebra and its applications
Date of publication: 2011
Journal article
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A differential approach for bounding the index of graphs under perturbations
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Date: 201103
Report
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Edgedistanceregular graphs
Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Date: 20110311
Report
Read the abstract Access to the full text Share Reference managersEdgedistanceregularity is a concept recently introduced by the authors which is similar to that of distanceregularity, 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 edgedistanceregular when it is distanceregular 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 edgedistanceregular if and only if its kincidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distanceregular graphs is proved, so giving a quasispectral characterization of edgedistanceregularity. Finally, it is shown that every nonbipartite graph which is both distanceregular and edgedistanceregular is a generalized odd graph. 
Edgedistanceregularity
Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
International Workshop on Network Topologies
Presentation's date: 20110714
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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: 20110621
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Edgedistanceregular 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: 20110831
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Graphs, Friends and Acquaintances
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
Date: 20100423
Report
Read the abstract Access to the full text Share Reference managersAs 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 distanceregular graphs and completely regular codes, and finally the study of topological proprieties of interconnection networks. 
On almost distanceregular 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 View Share Reference managersDistanceregular 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 distanceregular 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 distanceregular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walkregular 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 distanceregularity and walkregularity called mwalkregularity. Another studied concept is that of mpartial distanceregularity or, informally, distanceregularity up to distance m. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distanceregularity, such as their common generalization of ( ,m)walkregularity. We introduce the concepts of punctual distanceregularity and punctual walkregularity 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 distanceregular becomes whole distanceregular. We also give several characterizations of punctually distanceregular graphs that are generalizations of the spectral excess theorem. 
Characterizing (l, m)walkregular graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Linear algebra and its applications
Date of publication: 20101230
Journal article
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Grafs, amics i coneguts
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
Butlletí de la Societat Catalana de Matemàtiques
Date of publication: 2010
Journal article
Read the abstract Access to the full text Share Reference managersCom 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 distànciaregularitat 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 distànciaregulars i de codis completament regulars i, finalment, l’estudi de les propietats topològiques de les xarxes d’interconnexió. 
Characterizing (l,m)walkregular graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga, Ernest
Linear algebra and its applications
Date of publication: 2010
Journal article
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The geometry of tspreads in kwalkregular graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Journal of graph theory
Date of publication: 201008
Journal article
Read the abstract Access to the full text Share Reference managersA graph is walkregular if the number of closed walks of length rooted at a given vertex is a constant through all the vertices for all . For a walkregular graph G with d+1 different eigenvalues and spectrally maximum diameter D=d, we study the geometry of its dspreads, 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 threedimensional case) and we compute its parameters. Moreover, the results are generalized to the case of kwalkregular graphs, a family which includes both walkregular and distanceregular graphs, and their tspreads or vertices at distance t from each other. 
When almost distanceregularity attains distanceregularity
Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
French Combinatorial Conference
Presentation's date: 20100628
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Read the abstract Access to the full text Share Reference managersGenerally speaking, `almost distanceregular graphs' are graphs which share some, but not necessarily all, regularity properties that characterize distanceregular graphs. In this paper we rst propose four basic di erent (but closely related) concepts of almost distanceregularity. In some cases, they coincide with concepts introduced before by other authors, such as walkregular graphs and partially distanceregular 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 distanceregular graph. Our study focuses on nding out when almost distance regularity leads to distanceregularity. 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 socalled spectral excess theorem for distanceregular graphs. 
Dual concepts of almost distanceregularity and the spectral excess theorem
Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
International Workshop on Optimal Network Topologies
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A taste of duality in almost distanceregularity
Fiol Mora, Miquel Àngel; Dalfo Simo, Cristina; Van Dam, Edwin R; Garriga Valle, Ernest
SwedishCatalan Conference in Mathematics
Presentation's date: 20100917
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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: 20100610
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On almost distanceregular graphs
Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
Joint Mathematical Conference CSASC
Presentation's date: 20100125
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On tcliques in kwalkregular graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic notes in discrete mathematics
Date of publication: 200908
Journal article
Read the abstract View Share Reference managersA graph is walkregular if the number of cycles of length rooted at a given vertex is a constant through all the vertices. For a walkregular graph G with d+1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its dcliques, 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 kwalkregular graphs, a family which includes both walkregular and distanceregular graphs, and their tcliques 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
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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
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On tcliques in kwalkregular graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
EUROCOMB'09: European Conference on Combinatorics, Graph Theory and Applicactions
Presentation's date: 20090910
Presentation of work at congresses
Read the abstract View Share Reference managersA graph is walkregular if the number of cycles of length rooted at a given vertex is a constant through all the vertices. For a walkregular graph G with d+1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its dcliques, 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 kwalkregular graphs, a family which includes both walkregular and distanceregular graphs, and their tcliques or vertices at distance t from each other. 
On kwalkregular graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
British Combinatorial Conference
Presentation of work at congresses
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Les idees en didàctica de la matemàtica de Lluís Santaló
Dalfo Simo, Cristina
Date of publication: 200907
Book chapter
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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: 200907
Book
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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: 200901
Journal article
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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
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On kWalkRegular graphs
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic journal of combinatorics
Date of publication: 200904
Journal article
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The generalized hierarchical product of graphs
Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
Discrete mathematics
Date of publication: 200906
Journal article
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Extremal and optimization problems in graph theory and combinatorics: Applications to the analysis and algorithms in communication networks (accepted)
Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
Participation in a competitive project
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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
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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
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