Now showing items 21-40 of 43

• 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 ...
• New small regular graphs of girth 5 ﻿

(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 ...
• 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 identifying codes in line digraphs ﻿

(2019)
Conference report
Open Access
• 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 ...
• On the connectivity and restricted edge-connectivity of 3-arc graphs ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
A 3−arc of a graph G is a 4-tuple (y, a, b, x) of vertices such that both (y, a, b) and (a, b, x) are paths of length two in G. Let ←→G denote the symmetric digraph of a graph G. The 3-arc graph X(G) of a given graph G is ...
• On the connectivity and superconnected graphs with small diameter ﻿

(2010-03-06)
Article
Restricted access - publisher's policy
In this paper, first we prove that any graph G is 2-connected if diam (G)≤ g-1 for even girth g, and for odd girth g and maximum degree $\Delta$ ≤ 2$\delta$-1 where $\delta$ is the minimum degree. Moreover, we prove that ...
• On the connectivity of semiregular cages ﻿

(2010-08)
Article
Restricted access - publisher's policy
An ({r,r+1};g)-cage is a graph with degree set {r,r+1}, girth g, and with the smallest possible order; every such graph is called a semiregular cage. In this article, semiregular cages are shown to be maximally edge-connected ...
• On the restricted arc-connectivity of s-geodetic digraphs ﻿

(2010-10)
Article
Restricted access - publisher's policy
For a strongly connected digraph D the restricted arc-connectivity λ′(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D - S has a non-trivial strong component D₁ such that D-V ...
• On the restricted connectivity and superconnectivity in graphs with given girth ﻿

(2007-03)
Article
Restricted access - publisher's policy
The restricted connectivity κ′(G)κ′(G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex uu has all its neighbors in X; the superconnectivity κ1(G)κ1(G) ...
• On the superconnectivity in graphs with odd girth g and even girth h ﻿

(2009-09)
Article
Restricted access - publisher's policy
A maximally connected graph G of minimum degree δ is said to be superconnected (for short super-κ) if all disconnecting sets of cardinality δ are the neighborhood of some vertex of degree δ. Sufficient conditions on the ...
• On the λ'-optimality of s-geodetic digraphs ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
For a strongly connected digraph D the restricted arc-connectivity λ'(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D − S has a non trivial strong component D1 such that D − V ...
• Rainbow connectivity of Moore cages of girth 6 ﻿

(2018-12-11)
Article
Open Access
Let be an edge-colored graph. A path of is said to be rainbow if no two edges of have the same color. An edge-coloring of is a rainbow-coloring if for any two distinct vertices and of there are at least internally ...
• Small regular graphs of girth 7 ﻿

(2015-07-01)
Article
Open Access
In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. ...
• Some properties of semiregular cages ﻿

(2010)
Article
Restricted access - publisher's policy
A graph with degree set {r,r + 1} is said to be semiregular. A semiregular cage is a semiregular graph with given girth g and the least possible order. First, an upper bound on the diameter of semiregular graphs with girth ...
• Subdivisions in a bipartite graph ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
Given a bipartite graph G with m and n vertices, respectively,in its vertices classes, and given two integers s, t such that 2 ≤ s ≤ t, 0 ≤ m−s ≤ n−t, and m+n ≤ 2s+t−1, we prove that if G has at least mn−(2(m−s)+n−t) edges ...
• Sufficient conditions for a digraph to admit a (1,=l)-identifying code ﻿

(2019)
Article
Open Access
A (1, = )-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most  have distinct closed in-neighbourhoods within C. In this paper, we give some ...
• Superconnectivity of graphs with odd girth g and even girth h ﻿

(2009-09)
Conference report
Restricted access - publisher's policy
A maximally connected graph G of minimum degree δ is said to be superconnected (for short super-κ) if all disconnecting sets of cardinality δ are the neighborhood of some vertex of degree δ. Sufficient conditions on the ...