Now showing items 1-7 of 7

• #### 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 ...
• #### 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 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 vulnerability of some families of graphs ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
The toughness of a noncomplete graph G is defined as τ (G) = min{|S|/ω(G − S)}, where the minimum is taken over all cutsets S of vertices of G and ω(G − S) denotes the number of components of the resultant graph G − S by ...
• #### 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 ...
• #### 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 ...
• #### 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 ...