• A construction of Small (q-1)-Regular Graphs of Girth 8 

      Abreu, Marien; Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Labbate, D. (2015-04-21)
      Artículo
      Acceso abierto
      In this note we construct a new infinite family of (q - 1)-regular graphs of girth 8 and order 2q(q - 1)(2) for all prime powers q >= 16, which are the smallest known so far whenever q - 1 is not a prime power or a prime ...
    • A construction of small regular bipartite graphs of girth 8 

      Balbuena Martínez, Maria Camino Teófila (2009-01)
      Artículo
      Acceso abierto
      Let q be a prime a power and k an integer such that 3 ≤ k ≤ q. In this paper we present a method using Latin squares to construct adjacency matrices of k-regular bipartite graphs of girth 8 on $2(kq^{2}-q)$ vertices. Some ...
    • A family of mixed graphs with large order and diameter 2 

      Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Miller, Mirka; Zdimalova, Maria (2017-02)
      Artículo
      Acceso abierto
      A mixed regular graph is a connected simple graph in which each vertex has both a fixed outdegree (the same indegree) and a fixed undirected degree. A mixed regular graphs is said to be optimal if there is not a mixed ...
    • A sufficient condition for Pk-path graphs being r-connected 

      Balbuena Martínez, Maria Camino Teófila; García-Vázquez, Pedro (2007-08)
      Artículo
      Acceso abierto
      Given an integer k≥1 and any graph G; the path graph $P_k(G)$ has for vertices the paths of length k in G, and two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of ...
    • A sufficient degree condition for a graph to contain all trees of size k 

      Balbuena Martínez, Maria Camino Teófila; Márquez, Alberto; Portillo, Jose Ramón (Springer Verlag, 2011-01)
      Artículo
      Acceso restringido por política de la editorial
      The Erdős-Sós conjecture says that a graph G on n vertices and number of edges e(G) > n(k− 1)/2 contains all trees of size k. In this paper we prove a sufficient condition for a graph to contain every tree of size k ...
    • 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)
      Artículo
      Acceso abierto
      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 ...
    • Adjacency matrices of polarity graphs and of other C4-free graphs of large size 

      Abreu, M.; Balbuena Martínez, Maria Camino Teófila; Labbate, D. (2010)
      Artículo
      Acceso restringido por política de la editorial
      In this paper we give a method for obtaining the adjacency matrix of a simple polarity graph $G_q$ from a projective plane PG(2,q), where q is a prime power. Denote by ex(n;C₄) the maximum number of edges of a graph on n ...
    • An alternate description of a (q + 1; 8)-cage 

      Abreu, Marien; Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Labbate, Domenico (2018-12)
      Artículo
      Acceso abierto
      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.
    • Bounds on the k-restricted arc connectivity of some bipartite tournaments 

      Balbuena Martínez, Maria Camino Teófila; González Moreno, Diego; Olsen, Mika (2018-08-15)
      Artículo
      Acceso abierto
      For k¿=¿2, a strongly connected digraph D is called -connected if it contains a set of arcs W such that contains at least k non-trivial strong components. The k-restricted arc connectivity of a digraph D was defined by ...
    • Characterizing identifying codes from the spectrum of a graph or digraph 

      Balbuena Martínez, Maria Camino Teófila; Dalfó Simó, Cristina; Martínez Barona, Berenice (Elsevier, 2019-06-01)
      Artículo
      Acceso abierto
      A -identifying code in digraph D is a dominating subset C of vertices of D, such that all distinct subsets of vertices of D with cardinality at most l have distinct closed in-neighborhoods within C. As far as we know, it ...
    • Characterizing identifying codes through the spectrum of a graph or digraph 

      Balbuena Martínez, Maria Camino Teófila; Dalfó Simó, Cristina; Martínez Barona, Berenice (2017)
      Texto en actas de congreso
      Acceso abierto
    • Connectivity: properties and structure 

      Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel (CRC Press Taylor & Francis Group, 2013-12-05)
      Capítulo de libro
      Acceso abierto
      Connectivity is one of the central concepts of graph theory, from both a theoret- ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice max-min characterization results, ...
    • Constructions of small regular bipartite graphs of girth 6 

      Araujo Pardo, M. Gabriela; Balbuena Martínez, Maria Camino Teófila (2011-03)
      Artículo
      Acceso restringido por política de la editorial
      In this article, some structures in the projective plane of order q are found which allow us to construct small k - regular balanced bipartite graphs of girth 6 for all k ≤ q. When k = q, the order of these q-regular ...
    • Edge-superconnectivity of semiregular cages with odd girth 

      Balbuena Martínez, Maria Camino Teófila; Salas, Julián; González-Moreno, Diego (Iniciativa Digital Politècnica, 2011)
      Texto en actas de congreso
      Acceso abierto
      A graph is said to be edge-superconnected if each minimum edge-cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a {d, d + 1}- semiregular graph if all its vertices have ...
    • Estudios sobre algunas nuevas clases de conectividad condicional en grafos dirigidos 

      Balbuena Martínez, Maria Camino Teófila (Universitat Politècnica de Catalunya, 1995-11-24)
      Tesis
      Acceso abierto
      La conectividad condicional, definida por Harary en 1983, mide el mínimo número de vértices (o ramas) que hay que eliminar de un grafo o digrafo de forma que todas las componentes conexas resultantes tengan una propiedad ...
    • Further topics in connectivity 

      Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel (CRC Press Taylor & Francis Group, 2013-12-05)
      Capítulo de libro
      Acceso abierto
      Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edge-connectivity. First, we describe results ...
    • Identifying codes from the spectrum of a graph or digraph 

      Balbuena Martínez, Maria Camino Teófila; Dalfó Simó, Cristina; Martínez Barona, Berenice (LaBRI, 2019)
      Texto en actas de congreso
      Acceso abierto
    • Identifying codes in line digraphs 

      Balbuena Martínez, Maria Camino Teófila; Dalfó Simó, Cristina; Martínez Barona, Berenice (Elsevier, 2020-10-15)
      Artículo
      Acceso restringido por política de la editorial
      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 ...
    • 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)
      Artículo
      Acceso abierto
      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 ...
    • Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices 

      Balbuena Martínez, Maria Camino Teófila (2008-11)
      Artículo
      Acceso abierto
      Let q be a prime power and r=0,1...,q−3. Using the Latin squares obtained by multiplying each entry of the addition table of the Galois field of order q by an element distinct from zero, we obtain the incidence matrices ...