Now showing items 1-20 of 34

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

(2015-04-21)
Article
Open Access
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 ﻿

(2009-01)
Article
Open Access
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 ...
• #### Adjacency matrices of polarity graphs and of other C4-free graphs of large size ﻿

(2010)
Article
Restricted access - publisher's policy
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 ...
• #### A family of mixed graphs with large order and diameter 2 ﻿

(2017-02)
Article
Open Access
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 ﻿

(2007-08)
Article
Open Access
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 ﻿

(Springer Verlag, 2011-01)
Article
Restricted access - publisher's policy
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 ...
• #### Bounds on the k-restricted arc connectivity of some bipartite tournaments ﻿

(2018-08-15)
Article
Restricted access - publisher's policy
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 ﻿

(Elsevier, 2019-06-01)
Article
Restricted access - publisher's policy
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 ﻿

(2017)
Conference report
Open Access
• #### Connectivity: properties and structure ﻿

(CRC Press Taylor & Francis Group, 2013-12-05)
Part of book or chapter of book
Open Access
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 ﻿

(2011-03)
Article
Restricted access - publisher's policy
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 ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
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 ﻿

(Universitat Politècnica de Catalunya, 1995-11-24)
Doctoral thesis
Open Access
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 ﻿

(CRC Press Taylor & Francis Group, 2013-12-05)
Part of book or chapter of book
Open Access
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 ...
• #### Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices ﻿

(2008-11)
Article
Open Access
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 ...
• #### Kernels and partial line digraphs ﻿

(Elsevier, 2010-10)
Article
Restricted access - publisher's policy
Let D = (V,A) be a digraph with minimum in-degree 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 ...
• #### Locating-dominating sets and identifying codes in Graphs of Girth at least 5 ﻿

(2015-04-29)
Article
Open Access
Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified ...
• #### New families of graphs without short cycles and large size ﻿

(2010-06-06)
Article
Restricted access - publisher's policy
We denote by ex \$(n; {C^3,C^4,…Cs})\$ or fs(n) the maximum number of edges in a graph of order n and girth at least s+1. First we give a method to transform an n-vertex graph of girth g into a graph of girth at least g-1 ...
• #### On a conjecture on the order of cages with a given girth pair ﻿

(2015-08-20)
Article
Restricted access - publisher's policy
A (k; g, h)-graph is a k-regular graph of girth pair (g, h) where g is the girth of the graph, h is the length of a smallest cycle of different parity than g and g < h. A (k; g, h)-cage is a (k; g, h)-graph with the least ...
• #### On the acyclic disconnection and the girth ﻿

(2015-05-11)
Article
Open Access
The acyclic disconnection, (omega) over right arrow (D), of a digraph D is the maximum number of connected components of the underlying graph of D - A(D*), where D* is an acyclic subdigraph of D. We prove that (omega) over ...