Now showing items 1-20 of 28

• #### A differential approach for bounding the index of graphs under perturbations ﻿

(2011-09-02)
Article
Open Access
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 ...
• #### A differential approach for bounding the index of graphs under perturbations ﻿

(2011-03)
External research report
Open Access
• #### A new approach to the spectral excess theorem for distance-regular graphs ﻿

(2009-04-01)
Article
Open Access
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 ...
• #### Aprenentatge de càlcul ﻿

(Edicions UPC, 2002)
Book
Conté: 1. Successions, continuïtat i derivació. 2. Integració i sèries.
• #### A simple proof of the spectral excess theorem for distance-regular graphs ﻿

(Elsevier, 2010-04-15)
Article
Restricted access - publisher's policy
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 ...
• #### Characterizing (l,m)-walk-regularity ﻿

(2009-05)
Article
Open Access
A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ ...
• #### Combinatorial vs. algebraic characterizations of pseudo-distance-regularity around a set ﻿

(2009-06)
External research report
Open Access
Given a simple connected graph $\Gamma$ and a subset of its vertices $C$, the pseudo-distance-regularity around $C$ generalizes, for not necessarily regular graphs, the notion of completely regular code. Up to now, most ...
• #### Contribució a la teoria espectral de grafs problemes mètrics i distància-regularitat ﻿

(Universitat Politècnica de Catalunya, 1997-12-12)
Doctoral thesis
Open Access
• #### Dual concepts of almost distance-regularity and the spectral excess theorem ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
Generally speaking, ‘almost distance-regular’ graphs are graphs that share some, but not necessarily all, regularity properties that characterize distance-regular graphs. In this paper we first propose two dual concepts ...
• #### Edge distance-regular graphs ﻿

(2011)
Article
Open Access
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 ...
• #### Edge-distance-regular graphs ﻿

(2011-03-11)
External research report
Open Access
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 ...
• #### Edge-distance-regular graphs ﻿

(2011)
Article
Restricted access - publisher's policy
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 ...
• #### Moments in graphs ﻿

(2013)
Article
Open Access
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 ...
• #### Number of walks and degree powers in a graph ﻿

(2006-04)
Article
Open Access
This letter deals with the relationship between the total number of k-walks in a graph, and the sum of the k-th powers of its vertex degrees. In particular, it is shown that the sum of all k-walks is upper bounded by the ...
• #### On Almost Distance-Regular Graphs ﻿

(2010-03-12)
External research report
Open Access
• #### On almost distance-regular graphs ﻿

(2010)
Article
Restricted access - publisher's policy
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 ...
• #### On k-Walk-Regular Graphs ﻿

(2008-08)
Article
Open Access
Considering a connected graph $G$ with diameter $D$, we say that it is \emph{$k$-walk-regular}, for a given integer $k$ $(0\leq k \leq D)$, if the number of walks of length $\ell$ between vertices $u$ and $v$ only depends ...
• #### On outindependent subgraphs of strongly regular graphs ﻿

(Taylor & Francis, 2006)
Article
Open Access
An outindependent subgraph of a graph G, with respect to an independent vertex subset C¿¿V, is the subgraph GC induced by the vertices in V\¿C. We study the case when G is strongly regular, where the results of de Caen ...
• #### On t-cliques in k-walk-regular graphs ﻿

(2009-08)
Article
Restricted access - publisher's policy
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 = ...
• #### On t-cliques in k-walk-regular graphs ﻿

(Université de Bourdeaux, 2009)
Conference report
Open Access