Recent Submissions

  • 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 Gutierrez, Victor (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 ...
  • An alternate description of a (q + 1; 8)-cage 

    Abreu, Marien; Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Labbate, Domenico (2018-12)
    Article
    Open Access
    Let q >= 2 be a prime power. In this note we present an alternate description of the known (q + 1; 8)-cages which has allowed us to construct small (k; g)–graphs for k =q, q-1, and g = 7; 8 in other papers on this same topic.
  • New small regular graphs of girth 5 

    Abajo, E.; Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Bendala García, Manuel Francisco (2017-08)
    Article
    Open Access
    A (k,g)-graph is a k-regular graph with girth g and a (k,g)-cage is a (k,g)-graph with the fewest possible number of vertices. The cage problem consists of constructing (k,g)-graphs of minimum order n(k,g). We focus on ...
  • The p-restricted edge-connectivity of Kneser graphs 

    Balbuena Martínez, Maria Camino Teófila; Marcote Ordax, Francisco Javier (Elsevier, 2019-02-15)
    Article
    Open Access
    Given a connected graph G and an integer 1¿=¿p¿=¿¿|V(G)|/2¿, a p-restricted edge-cut of G is any set of edges S¿¿¿E(G), if any, such that is not connected and each component of has at least p vertices; and the p-restricted ...
  • Improving bounds on the order of regular graphs of girth 5 

    Abajo Casado, Encarnación; Balbuena Martínez, Maria Camino Teófila; Bendala García, Manuel Francisco; Marcote Ordax, Francisco Javier (2019-10-01)
    Article
    Open Access
    A -graph is a -regular graph with girth and a -cage is a -graph with the fewest possible number of vertices . Constructing -cages and determining the order are both very hard problems. For this reason, an intensive line ...
  • About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs 

    Balbuena Martínez, Maria Camino Teófila; Galeana Sánchez, Hortensia; Guevara Aguirre, Nucuy-kak (2019-06)
    Article
    Open Access
    Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 = l = k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial ...
  • An analogue of Vosper's theorem for extension fields 

    Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles (2017-11-01)
    Article
    Open Access
    We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result ...
  • Forbidden subgraphs in the norm graph 

    Ball, Simeon Michael; Pepe, Valentina (2016-04-06)
    Article
    Open Access
    We show that the norm graph with n vertices about View the MathML source edges, which contains no copy of the complete bipartite graph Kt,(t-1)!+1, does not contain a copy of Kt+1,(t-1)!-1.
  • On the relation between graph distance and Euclidean distance in random geometric graphs 

    Díaz Cort, Josep; Dieter Wilhelm, Mitsche; Perarnau Llobet, Guillem; Pérez Giménez, Xavier (2016-09-01)
    Article
    Open Access
    Given any two vertices u, v of a random geometric graph G(n, r), denote by dE(u, v) their Euclidean distance and by dE(u, v) their graph distance. The problem of finding upper bounds on dG(u, v) conditional on dE(u, v) ...
  • Revisiting Kneser’s theorem for field extensions 

    Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles (2017-05-31)
    Article
    Open Access
    A Theorem of Hou, Leung and Xiang generalised Kneser’s addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all ...

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