Garriga Valle, Ernest
Total activity: 71
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Department of Applied Mathematics IV
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egarrigama4.upc.edu
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    Moments in graphs  Open access

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

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    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)

  • 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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    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

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    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

  • 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

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    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

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    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.

  • 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

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    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.

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    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
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    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

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    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

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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: 2011-06-21
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  • 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
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  • Combinatorial vs. Algebraic Characterizations of Completely Pseudo-Regular Codes

     Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Electronic journal of combinatorics
    Date of publication: 2010-03-08
    Journal article

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  • A simple proof of the spectral excess theorem for distance-regular graphs

     Fiol Mora, Miquel Àngel; Gago Alvarez, Silvia; Garriga Valle, Ernest
    Linear algebra and its applications
    Date of publication: 2010-04-15
    Journal article

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    The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the so-called pseudo-distance-regularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role.

  • 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

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  • 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

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    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.

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    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

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    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.

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    On Almost Distance-Regular Graphs  Open access

     Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
    Date: 2010-03-12
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  • 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
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    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
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    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.

  • 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
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  • Local spectrum of the subconstituents and completely pseudo-regular codes

     Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2010-07-08
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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: 2010-06-10
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  • 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
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  • 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
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    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
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  • Number of walks and degree powers in a graph

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Discrete mathematics
    Date of publication: 2009-04
    Journal article

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  • 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

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  • Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes

     Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Electronic journal of combinatorics
    Date of publication: 2009-07
    Journal article

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  • 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

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    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.

  • 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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  • COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

     Moragas Vilarnau, Jordi; Comellas Padro, Francesc de Paula; López Masip, Susana Clara; Gago Alvarez, Silvia; Pérez Mansilla, Sonia; Mitjana Riera, Margarida; Llado Sanchez, Anna; Barriere Figueroa, Eulalia; Zaragoza Monroig, Maria Luisa; Garriga Valle, Ernest; Espona Dones, Margarida; Rius Font, Miquel; Aroca Farrerons, Josep Maria; Aguilo Gost, Francisco de Asis Luis; Muñoz Lopez, Francisco Javier; Gomez Marti, Jose; Miralles De La Asuncion, Alicia; Dalfo Simo, Cristina; Cámara Vallejo, Marc; 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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  • Algunas aplicaciones de polinomios ortogonales de variable discreta a grafos y códigos

     Garriga Valle, Ernest
    Seminario de Matemática Discreta
    Presentation's date: 2008-09-09
    Presentation of work at congresses

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  • Algunas aplicaciones de polinomios ortogonales de variable discreta a grafos y códigos

     Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Seminario de Matemática Discreta
    Presentation's date: 2008-09-09
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  • Algunas aplicaciones de polinomios octogonales de variable discreta a grafos y códigos

     Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Jornadas de Matemática Discreta y Algorítmica
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    A new Approach to the Spectral Excess Theorem for Distance-Regular Graphs  Open access

     Gago Alvarez, Silvia; Garriga Valle, Ernest; Fiol Mora, Miquel Àngel
    Workshop on Spectral Graph Theory with applications on Computer Science, Combinatorial Optimization and Chemistry
    Presentation's date: 2008-12-01
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    The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph $\Gamma$ with $d+1$ different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices.\ The original approach, due to Fiol and Garriga in $1997$, was obtained in a wide context from a local point of view, so giving a characterization of the so-called pseudo-distance-regularity around a vertex.\ In this paper we present a new simple method based in a global point of view, and where the mean degree of the distance-$d$ graph $\Gamma_d$ plays an essential role.

  • Spectral and Geometric Properties of k-Walk-Regular Graphs

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Electronic notes in discrete mathematics
    Date of publication: 2007-08
    Journal article

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  • Una experiencia docente orientada a incrementar el trabajo personal del estudiante

     Otero Calviño, Beatriz; Martí Farré, Jaume; Garriga Valle, Ernest; Alonso Maleta, Maria Aranzazu; LLUIS, PRAT; Prat Viñas, Luis
    Jornadas de Enseñanza Universitaria de la Informática
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  • On outindependent subgraphs of strongly regular graphs

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Linear and multilinear algebra
    Date of publication: 2006-03
    Journal article

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  • On the spectrum of an extremal graph with four eigenvalues

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Discrete mathematics
    Date of publication: 2006-09
    Journal article

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  • Number of Walks and Degree Powers in a Graph*

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Date: 2006-04
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  • Combinatòria, Teoria de Grafs i Aplicacions

     Serra Albo, Oriol; Aguilo Gost, Francisco de Asis Luis; Andrés Yebra, José Luis; Balbuena Martinez, Maria Camino Teofila; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Marcote Ordax, Francisco Javier; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Moragas Vilarnau, Jordi; Montejano Cantoral, Amanda; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Zaragoza Monroig, Maria Luisa
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  • Avoiding monocoloured triangles when colouring Kn

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Andres Yebra, Jose Luis
    Date: 2004-08
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  • An algebraic characterization of completely regular codes in distance-regular graphs

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    SIAM journal on discrete mathematics
    Date of publication: 2002-03
    Journal article

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  • Pseudo-strong regularity around a set

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    Linear and multilinear algebra
    Date of publication: 2002-03
    Journal article

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  • Aprenentatge de càlcul-1. successions, contiuïtat i derivació.

     Aguilo Gost, Francisco de Asis Luis; Miralles De La Asuncion, Alicia; Garriga Valle, Ernest; Barguilla Navarrete, Jorge
    Date of publication: 2002-09-30
    Book

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  • Aprenentatge de Càlcul -2. Integració i sèries.

     Aguilo Gost, Francisco de Asis Luis; Garriga Valle, Ernest; Miralles De La Asuncion, Alicia; Barguilla Navarrete, Jorge
    Date of publication: 2002-09-30
    Book

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  • Some algebraic characterization of completely regular and perfect codes

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

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  • Algebraic characterizations of completely regular codes

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
    SIAM journal on discrete mathematics
    Date of publication: 2001-10
    Journal article

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  • Boundary graphs: The limit case of a spectral property

     Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Andres Yebra, Jose Luis
    Discrete mathematics
    Date of publication: 2001-01
    Journal article

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