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

  • On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Pavlíková, Sona; Siran, Josef (Taylor & Francis, 2022-02-19)
    Article
    Restricted access - publisher's policy
    The universal adjacency matrix U of a graph G, with adjacency matrix A, is a linear combination of A, the diagonal matrix D of vertex degrees, the identity matrix I, and the all-1 matrix J with real coefficients, that is, ...
  • Optimization of eigenvalue bounds for the independence and chromatic number of graph powers 

    Abiad, Aida; Coutinho, Gabriel; Fiol Mora, Miquel Àngel; Nogueira, Bruno; Zeijlemaker, Shanne (2022-03)
    Article
    Open Access
    The k-thpower of a graph G=(V,E), G^k, is the graph whose vertex set is V and in which two distinct vertices are adjacent if and only if their distance in G is at most k. This article proves various eigenvalue bounds for ...
  • Some results on the laplacian spectra of Token graphs 

    Dalfó Simó, Cristina; Duque, Frank; Fabila Monroy, Ruy; Fiol Mora, Miquel Àngel; Huemer, Clemens; Trujillo Negrete, Ana Laura; Zaragoza Martínez, Francisco (Springer, 2021)
    Conference report
    Restricted access - publisher's policy
    We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent ...
  • On symmetric association schemes and associated quotient-polynomial graphs 

    Fiol Mora, Miquel Àngel; Penjic, Safet (2021-01-01)
    Article
    Open Access
    Let denote an undirected, connected, regular graph with vertex set , adjacency matrix , and distinct eigenvalues. Let denote the subalgebra of generated by . We refer to as the adjacency algebra of . In this paper we ...
  • On the Laplacian spectra of token graphs 

    Dalfó Simó, Cristina; Duque, Frank; Fabila Monroy, Ruy; Fiol Mora, Miquel Àngel; Huemer, Clemens; Trujillo Negrete, Ana Laura; Zaragoza Martínez, Francisco (Elsevier, 2021-09-15)
    Article
    Restricted access - publisher's policy
    We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever ...
  • New cyclic Kautz digraphs with optimal diameter 

    Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens (2021)
    Article
    Open Access
    We obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and out-degree, there is no other digraph with a smaller diameter. This new family of digraphs are called `modified cyclic ...
  • Spectra and eigenspaces of arbitrary lifts of graphs 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Pavlíková, Sona; Siran, Josef (2021-09)
    Article
    Open Access
    We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).
  • Trees whose even-degree vertices induce a path are antimagic 

    Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín (2020-05-01)
    Article
    Open Access
    An antimagic labeling of a connected 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 v is the sum of the labels ...
  • Uniform forcing and immune sets in graphs and hypergraphs 

    Fàbrega Canudas, José; Martí Farré, Jaume; Muñoz López, Francisco Javier (2021-12-31)
    Article
    Restricted access - publisher's policy
    Zero forcing is an iterative coloring process on a graph that has been widely used in such different areas as the modelling of propagation phenomena in networks and the study of minimum rank problems in matrices and graphs. ...
  • Bipartite biregular Moore graphs 

    Araujo Pardo, Gabriela; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; López Lorenzo, Nacho (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 ...
  • On d-Fibonacci digraphs 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (2021-10-03)
    Article
    Open Access
    The d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we ...
  • Decompositions of a rectangle into non-congruent rectangles of equal area 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; López Lorenzo, Nacho; Martínez Pérez, Álvaro (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 ...

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