### Recent Submissions

• #### The dilating method to obtain dense cayley digraphs on finite abelian groups ﻿

(2021-01-01)
Article
Open Access
A geometric method for obtaining an infinite family of Cayley digraphs of constant density on finite abelian groups is presented. The method works for any given degree d ≥ 2, and it is based on consecutive dilates of a ...
• #### Elimination properties for minimal dominating sets of graphs ﻿

(2020-01-01)
Article
Open Access
A dominating set of a graph is a vertex subset such that every vertexnot in the subset is adjacent to at least one in the subset. In this paper westudy whenever there exists a new dominating set contained (respectively, ...
• #### Identifying codes in line digraphs ﻿

(Elsevier, 2020-10-15)
Article
Restricted access - publisher's policy
Given an integer  = 1, a (1, = )-identifying code in a digraph is a dominating subset C of vertices such that all distinct subsets of vertices of cardinality at most ` have distinct closed in-neighbourhood within C. In ...
• #### Ciclos de Hamilton en redes de pasos commutativos y de paso fijo ﻿

(1988)
Article
Open Access
From a natural generalization to Z2 of the concept of congruence, it is possible to define a family of 2-regular digraphs that we call commutative-step networks. Particular examples of such digraphs are the cartesian product ...
• #### Caterpillars are antimagic ﻿

(2021-01-21)
Article
Restricted access - publisher's policy
An antimagic labeling of a graph G is a bijection from the set of edges E(G) to {1,2,…,|E(G)|}, such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to the ...
• #### Neighbor-locating colorings in graphs ﻿

(2020-02-02)
Article
Open Access
A k-coloring of a graph G is a k-partition of into independent sets, called colors. A k-coloring is called neighbor-locating if for every pair of vertices belonging to the same color , the set of colors of the neighborhood ...
• #### 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 ...
• #### 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 ...
• #### A new class of polynomials from the spectrum of a graph, and its application to bound the k-independence number ﻿

(Elsevier, 2020-11-15)
Article
Restricted access - publisher's policy
The k-independence number of a graph is the maximum size of a set of vertices at pairwise distance greater than k. A graph is called k-partially walk-regular if the number of closed walks of a given length l = k, rooted ...
• #### New Moore-like bounds and some optimal families of abelian Cayley mixed graphs ﻿

(2020-06)
Article
Open Access
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of Abelian groups. Such groups can be ...
• #### Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups ﻿

(Elsevier, 2020-07-15)
Article
Restricted access - publisher's policy
In this paper, we present a method to obtain regular (or equitable) partitions of Cayley (di)graphs (that is, graphs, digraphs, or mixed graphs) of permutation groups on n letters. We prove that every partition of the ...
• #### Equivalent characterizations of the spectra of graphs and applications to measures of distance-regularity ﻿

(2020-09)
Article
Open Access
The spectrum of a graph usually provides a lot of information about its combinatorial structure. Moreover,from the spectrum, the so-called predistance polynomials can be defined, as a generalization, for any graph, of the ...