Now showing items 1-20 of 82

• #### 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 general method to obtain the spectrum and local spectra of a graph from its regular partitions ﻿

(2020-07-12)
Article
Open Access
It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also ...
• #### 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 general family of mixed graphs ﻿

(2019-01-11)
Article
Open Access
A new general family of mixed graphs is presented, which generalizes both the pancake graphs and the cycle prefix digraphs. The obtained graphs are vertex transitive and, for some values of the parameters, they constitute ...
• #### A note on a new general family of deterministic hierarchical networks ﻿

(2019-06-01)
Article
Open Access
Hierarchical network; Small-word; Scale-free; Routing algorithm; Diameter; Clustering
• #### 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 ...
• #### A survey on the missing Moore graph ﻿

(Elsevier, 2019)
Article
Open Access
This is a survey on some known properties of the possible Moore graph (or graphs) ¿ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition ...
• #### 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 ...
• #### An algebraic approach to lifts of digraphs ﻿

(2019-09)
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 improved Moore bound and some new optimal families of mixed Abelian Cayley graphs ﻿

(2020-10)
Article
Restricted access - publisher's policy
We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can ...
• #### 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 ...
• #### Bipartite biregular Moore graphs ﻿

(2021-11)
Article
Restricted access - publisher's policy
A bipartite graph G = (V, E) with V = V1 ¿ V2 is biregular if all the vertices of a stable set Vi have the same degree ri for i = 1, 2. In this paper, we give an improved new Moore bound for an infinite family of such ...
• #### 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 $i\in [0,\ell]$ ...
• #### Characterizing identifying codes from the spectrum of a graph or digraph ﻿

(Elsevier, 2019-06-01)
Article
Open Access
A -identifying code in digraph D is a dominating subset C of vertices of D, such that all distinct subsets of vertices of D with cardinality at most l have distinct closed in-neighborhoods within C. As far as we know, it ...
• #### Characterizing identifying codes through the spectrum of a graph or digraph ﻿

(2017)
Conference report
Open Access
• #### Corrigendum to "Algebraic characterizations of regularity properties in bipartite graphs" Eur. J. Combin. 34 (2013) 1223-1231 ﻿

(2014)
Article
Open Access
• #### Cospectral digraphs from locally line digraphs ﻿

(Elsevier, 2016-07-01)
Article
Open Access
A digraph Gamma = (V, E) is a line digraph when every pair of vertices u, v is an element of V have either equal or disjoint in -neighborhoods. When this condition only applies for vertices in a given subset (with at least ...
• #### Decompositions of a rectangle into non-congruent rectangles of equal area ﻿

(2021-06)
Article
Restricted access - publisher's policy
In this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into k non-congruent rectangles of equal area? This problem is motivated by the so-called ‘Mondrian art problem’ that asks a ...
• #### Deterministic hierarchical networks ﻿

(2007-11-20)
Article
Open Access
Recently it has been shown that many networks associated with complex systems are small-world (they have both a large local clustering and a small diameter) and they are also scale-free (the degrees are distributed according ...