The research of COMBGRAPH deals with extremal problems in Combinatorics and Graph Theory. The study of discrete configurations (which optimize one or several parameters) is a main source of challenges. This project includes problems related to: the optimization of metric parameters of graphs, coloring and labeling problems, connectivity and reliability, configurations in graphs, symmetric structures, tilings, algorithm design, and signal processing techniques. All these problems are mainly motivated by applications in network design, analysis for communication protocols, multiprocessor systems, and complex networks. We use combinatorial and algebraic techniques in graph theory, Fourier analysis and polynomial and probabilistic methods in combinatorics, together with techniques close to the combinatorial nature of the problems under consideration. This project gathers the activity of a well-established research group with almost 30 years of experience and with international projection.

### 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 ...
• #### Combinatorial artists: counting, permutations, and other discrete structures in art ﻿

(Springer, 2021)
Part of book or chapter of book
Restricted access - publisher's policy
This chapter is motivated by a question I asked myself: “How can combinatorial structures be used in a work of art?” Immediately, other questions arose: Are there artists that work or think combinatorially? If so, what ...
• #### 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 ...
• #### Graph centralities and cascading failures in networks ﻿

(2019)
Conference report
Restricted access - publisher's policy
• #### 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 ...
• #### 3.000 passos fins al blau gel ﻿

(El Cep i la Nansa Edicions, 2019)
Part of book or chapter of book
Restricted access - publisher's policy
3.000 passos fins al blau gel es una animación generativa creada en Processing, inspirada en el poliedro de Albrecht Dürer. Es un proyecto de Eugènia Agustí y Lali Barrière desarrollado entre 2018 y 2019, en el contexto ...
• #### 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 ...