Now showing items 1-20 of 112

• #### Abelian Cayley digraphs with asymptotically large order for any given degree ﻿

(2016-04-29)
Article
Open Access
Abelian Cayley digraphs can be constructed by using a generalization to Z(n) of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, ...
• #### A Boolean algebra approach to the construction of snarks ﻿

(John Wiley & Sons, 1991)
Part of book or chapter of book
Open Access
This work deals with the construction of snarks, that is, cubic graphs that cannot be 3-edge-colored. A natural generalization of the concept of "color", that describes in a simple way the coloring ("0" or "1") of any set ...
• #### 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 discrete optimization problem in local networks and data alignment ﻿

(1987-06)
Article
Restricted access - publisher's policy
This paper presents the solution of the following optimization problem that appears in the design of double-loop structures for local networks and also in data memory, allocation and data alignment in SIMD processors. Consider ...
• #### A geometric approach to dense Cayley digraphs of finite Abelian groups ﻿

(2016)
Article
Open Access
We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. ...
• #### A geometric approach to dense Cayley digraphs of finite Abelian groups ﻿

(Elsevier, 2016)
Conference report
Open Access
We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related {\em minimum distance ...
• #### Algebraic characterizations of bipartite distance-regular graphs ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
Bipartite graphs are combinatorial objects bearing some interesting symmetries. Thus, their spectra—eigenvalues of its adjacency matrix—are symmetric about zero, as the corresponding eigenvectors come into pairs. Moreover, ...
• #### Algebraic characterizations of distance-regular graphs ﻿

(Elsevier, 2002)
Article
Open Access
We survey some old and some new characterizations of distance-regular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+1 distinct eigenvalues ...
• #### Algebraic Characterizations of Regularity Properties in Bipartite Graphs ﻿

(2013)
Article
Restricted access - publisher's policy
Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular if and only if its spectral excess (a number ...
• #### Algunos grafos compuestos ﻿

Article
Open Access
From two graphs $G_1$ and $G_2$ on $N_1$ and $N_2$ vertices respectively, the compound graph $G_1[G_2]$ on $N_1N_2$ vertices is obtained connecting $N_2$ copies of $G_1$ following the structure of $G_2$. We present in ...
• #### A mathematical model for dynamic memory networks ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
The aim of this paper is to bring together the work done several years ago by M.A. Fiol and the other authors to formulate a quite general mathematical model for a kind of permutation networks known as dynamic memories. A ...
• #### An algebraic approach to lifts of digraphs ﻿

(2018-12-07)
Article
Open Access
We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift Ga of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its ...
• #### An algebraic model for the storage of data in parallel memories ﻿

(Springer, 1989)
Part of book or chapter of book
Open Access
The use of SIMD computers requires efficient schemes of storage of data in order to have conflict-free acces in parallel computation. In this paper we restate the problem of finding such chemes in an algebraic context. ...
• #### An eigenvalue characterization of antipodal distance-regular graphs ﻿

(1997-11)
Article
Open Access
Let $\Gamma$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $\Gamma$ is an $r$-antipodal distance-regular graph if and only if the distance graph $\Gamma_d$ ...
• #### A new approach to gross error detection for GPS networks ﻿

(2019-05-29)
Article
Open Access
We present a new matrix-based approach to detect and correct gross errors in GPS geodetic control networks. The study is carried out by introducing a new matrix, whose entries are powers of a (real or complex) variable, ...
• #### 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 ...
• #### An improved upper bound for the order of mixed graphs ﻿

(2018-07)
Article
Open Access
A mixed graph G can contain both (undirected) edges and arcs (directed edges). Here we derive an improved Moore-like bound for the maximum number of vertices of a mixed graph with diameter at least three. Moreover, a ...
• #### An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs ﻿

(2014)
Conference report
Open Access
We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by ...
• #### A note on the order of iterated line digraphs ﻿

(Wiley, 2016-07-27)
Article
Open Access
Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal polynomial ...