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

  • Ciclos de Hamilton en redes de pasos commutativos y de paso fijo 

    Fiol Mora, Miquel Àngel; Andrés Yebra, José Luis (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 

    Agusti Cami, Maria Eugenia; Barrière Figueroa, Eulalia (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 

    Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín (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 

    Alcón, Liliana; Gutierrez, Marisa; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel (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 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (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 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; López Lorenzo, Nacho; Ryan, Joe (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 

    Fiol Mora, Miquel Àngel (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 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; López Lorenzo, Nacho (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 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (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 

    Fiol Mora, Miquel Àngel; Fàbrega Canudas, José; Diego Gutiérrez, Víctor (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 ...
  • Bounded queries to arbitrary sets 

    Lozano Bojados, Antoni (1991-09)
    External research report
    Open Access
    We prove that if P superA[k] = P superA[k+1] for some k and an arbitrary set A, then A is reducible to its complement under a relativized nondeterministic conjunctive reduction. This result shows the first known property ...
  • Relativized and positive separations of [delta sub 2 super p] and [fi sub 2 super p] 

    Lozano Bojados, Antoni; Torán Romero, Jacobo (1989)
    External research report
    Open Access

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