Browsing by Author "Balbuena Martínez, Maria Camino Teófila"
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A construction of Small (q1)Regular Graphs of Girth 8
Abreu, Marien; Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Labbate, D. (20150421)
Article
Open AccessIn 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 (200901)
Article
Open AccessLet 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 kregular 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 (201702)
Article
Open AccessA 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 Pkpath graphs being rconnected
Balbuena Martínez, Maria Camino Teófila; GarcíaVázquez, Pedro (200708)
Article
Open AccessGiven 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, 201101)
Article
Restricted access  publisher's policyThe ErdősSós 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, Nucuykak (201906)
Article
Open AccessLet D be a digraph of minimum indegree 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 C4free graphs of large size
Abreu, M.; Balbuena Martínez, Maria Camino Teófila; Labbate, D. (2010)
Article
Restricted access  publisher's policyIn 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 (201812)
Article
Open AccessLet 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, q1, and g = 7; 8 in other papers on this same topic. 
Bounds on the krestricted arc connectivity of some bipartite tournaments
Balbuena Martínez, Maria Camino Teófila; González Moreno, Diego; Olsen, Mika (20180815)
Article
Open AccessFor k¿=¿2, a strongly connected digraph D is called connected if it contains a set of arcs W such that contains at least k nontrivial strong components. The krestricted 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, 20190601)
Article
Restricted access  publisher's policyA 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 inneighborhoods 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)
Conference report
Open Access 
Connectivity: properties and structure
Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel (CRC Press Taylor & Francis Group, 20131205)
Part of book or chapter of book
Open AccessConnectivity 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 maxmin characterization results, ... 
Constructions of small regular bipartite graphs of girth 6
Araujo Pardo, M. Gabriela; Balbuena Martínez, Maria Camino Teófila (201103)
Article
Restricted access  publisher's policyIn 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 qregular ... 
Edgesuperconnectivity of semiregular cages with odd girth
Balbuena Martínez, Maria Camino Teófila; Salas, Julián; GonzálezMoreno, Diego (Iniciativa Digital Politècnica, 2011)
Conference report
Open AccessA graph is said to be edgesuperconnected if each minimum edgecut 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, 19951124)
Doctoral thesis
Open AccessLa 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, 20131205)
Part of book or chapter of book
Open AccessContinuing 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 edgeconnectivity. 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)
Conference report
Open Access 
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 (20191001)
Article
Open AccessA 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 (200811)
Article
Open AccessLet 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 ... 
Kernels and partial line digraphs
Balbuena Martínez, Maria Camino Teófila; Guevara, Mucuykak (Elsevier, 201010)
Article
Restricted access  publisher's policyLet D = (V,A) be a digraph with minimum indegree at least 1 and girth at least l+1, where l ≥ 1. In this work, the following result is proved: a digraph D has a (k,l)kernel if and only if its partial line digraph LD ...