Now showing items 21-28 of 28

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

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(2010)
Conference report
Restricted access - publisher's policy
• #### When almost distance-regularity attains distance-regularity ﻿

(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 ...