Now showing items 1-19 of 19

    • A Moore-like bound for mixed abelian Cayley graphs 

      López Lorenzo, Ignacio; Pérez Rosés, Hebert; Pujolàs Boix, Jordi (Elsevier B.V., 2016-09-26)
      We give an upper bound for the number of vertices in mixed abelian Cayley graphs with given degree and diameter.
    • A variant of the McKay-Miller-Siran construction for Mixed Graphs 

      López Lorenzo, Ignacio; Pérez Rosés, Hebert; Pujolàs Boix, Jordi; Zdimalovà, Maria (Elsevier B.V., 2016-09-27)
      The Degree/Diameter Problem is an extremal problem in graph theory with applications in network design. One of the main research areas in the Degree/Diameter Problem consists of finding large graphs whose order approach ...
    • An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; Ryan, Joe (Elsevier, 2020)
      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 ...
    • An improved upper bound for the order of mixed graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Elsevier B.V., 2018)
      A mixed graph G can contain both (undirected) edges and arcs (directed edges). Here we derive an improved Moore-like bound for the maximum number of vertices of a mixed graph with diameter at least three. Moreover, a ...
    • Bipartite biregular Moore graphs 

      Araujo Pardo, Martha Gabriela; Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Elsevier, 2021)
      A bipartite graph G=(V,E) with V=V1 U 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 graphs with ...
    • Decompositions of a rectangle into non-congruent rectangles of equal area 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; Martínez Pérez, Álvaro (Elsevier, 2021-06)
      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 ...
    • Degree/diameter problem for mixed graphs 

      López Lorenzo, Ignacio; Pérez Rosés, Hebert (Elsevier, 2015)
      The Degree/diameter problem asks for the largest graphs given diameter and maximum degree. This problem has been extensively studied both for directed and undirected graphs, ando also for special classes of graphs. In this ...
    • Equivalence classes of eccentric digraphs 

      López Lorenzo, Ignacio (Centre for Discrete Mathematics and Computing, 2017)
      The eccentric digraph operator takes a graph G (either directed or undirected) as a basis and transforms it into a digraph ED(G) with the same vertices as G and where there is an arc from a vertex u to a vertex v if and ...
    • Graph Theory-Based Characterization and Classification of Household Photovoltaics 

      Ceresuela, Jesús M.; Chemisana Villegas, Daniel; López Lorenzo, Ignacio (MDPI, 2021)
      With the clear goal of improving photovoltaic (PV) technology performance towards nearly-zero energy buildings, a graph theory-based model that characterizes photovoltaic panel structures is developed. An algorithm to ...
    • Mixed Moore Cayley graphs 

      López Lorenzo, Ignacio; Pérez Rosés, Hebert; Pujolàs Boix, Jordi (Elsevier, 2014-09-01)
      Cayley graphs are well known objects with interesting properties, also in the context of Moore graphs and digraphs. In $1978$ Bos\'ak extended Moore's property to the mixed setting (with arcs allowed along with edges), in ...
    • New Moore-Like Bounds and Some Optimal Families of Abelian Cayley Mixed Graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (2020-06-06)
      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 ...
    • New results for the Mondrian art problem 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Elsevier, 2021)
      The Mondrian problem consists of dissecting a square of side length n ∈ N into non-congruent rectangles with natural length sides such that the difference d(n) between the largest and the smallest areas of the rectangles ...
    • On bipartite-mixed graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Wiley, 2018-04-04)
      Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this arti- cle, we consider the case where such graphs are bipartite. As main results, we show that in this ...
    • On mixed almost Moore graphs of diameter two 

      López Lorenzo, Ignacio; Miret, Josep M. (Josep Maria) (Electronic Journal of Combinatorics, 2016-04-01)
      Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their ...
    • Properties of mixed Moore graphs of directed degree one 

      López Lorenzo, Ignacio; Pujolàs Boix, Jordi (Elsevier, 2015-04-01)
      Mixed graphs of order n such that for any pair of vertices there is a unique trail of length at most k between them are known as mixed Moore graphs. These extremal graphs may only exist for diameter k = 2 and certain ...
    • Sequence Mixed Graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Elsevier, 2017)
      A mixed graph can be seen as a type of digraph containing some edges (or two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line ...
    • The Degree/Diameter Problem for Mixed Abelian Cayley Graphs 

      López Lorenzo, Ignacio; Pérez Rosés, Hebert; Pujolàs Boix, Jordi (Elsevier, 2017-11-20)
      This paper investigates the upper bounds for the number of vertices in mixed abelian Cayley graphs with given degree and diameter. Additionally, in the case when the undirected degree is equal to one, we give a construction ...
    • The unique mixed almost moore graph with parameters k = 2, r = 2 and z = 1 

      Buset, Dominique; López Lorenzo, Ignacio; Miret, Josep M. (Josep Maria) (World Scientific Publishing, 2017-11-02)
      A natural upper bound for the maximum number of vertices in a mixed graph with maximum undirected degree r, maximum directed out-degree z and diameter k is given by the mixed Moore bound. Graphs with order attaining the ...
    • Triangle randomization for social network data anonymization 

      Brankovic, Ljiljana; López Lorenzo, Ignacio; Miller, Mirka; Sebé Feixas, Francesc (Society of Mathematicians, Physicists and Astronomers of Slovenia; Institute of Mathematics, Physics, and Mechanics; University of Primorska (Slovenia), 2014-06-27)
      In order to protect privacy of social network participants, network graph data should be anonymised prior to its release. Most proposals in the literature aim to achieve $k$-anonymity under specific assumptions about the ...