Now showing items 21-28 of 28

  • On the algebraic theory of pseudo-distance-regulariry around a set 

    Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (Elsevier, 1999-09)
    Article
    Restricted access - publisher's policy
    Let C be a connected graph with vertex set V, adjacency matrix A, positive eigenvector and corresponding eigenvalue 0. A natural generalization of distance-regularity around a vertex subset C V , which makes sense ...
  • On the local spectra of the subconstituents of a vertex set and completely pseudo-regular codes 

    Cámara Vallejo, Marc; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (2014-10-30)
    Article
    Restricted access - publisher's policy
    In this paper we study the relation between the local spectrum of a vertex set C and the local spectra of its subconstituents. In particular, it is shown that, when C is a completely regular code, such spectra are uniquely ...
  • Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes 

    Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Fàbrega Canudas, José; Cámara Vallejo, Marc (2000-08)
    Article
    Open Access
    We present some related families of orthogonal polynomials of a discrete variable and survey some of their applications in the study of (distance-regular) graphs and (completely regular) codes. One of the main peculiarities ...
  • The alternating and adjacency polynomials, and their relation with the spectra and diameters of graphs 

    Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (Elsevier Science Publishers B. V., 1998-10)
    Article
    Open Access
    Let Γ be a graph on n vertices, adjacency matrix A, and distinct eigenvalues λ > λ_1 > λ_2 > · · · > λ_d. For every k = 0,1, . . . ,d −1, the k-alternating polynomial P_k is defined to be the polynomial of degree k and norm |
  • The geometry of t-cliques in k-walk-regular graphs 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (2008-09)
    Article
    Open Access
    A graph is walk-regular if the number of cycles of length $\ell$ 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 ...
  • The geometry of t-spreads in k-walk-regular graphs 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (Wiley InterScience, 2010-08)
    Article
    Open Access
    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 ...
  • When almost distance regularity attains distance regularity 

    Dalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (2010)
    Conference report
    Restricted access - publisher's policy
  • When almost distance-regularity attains distance-regularity 

    Dalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (2010)
    Conference report
    Open Access
    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 ...