Weak-Rupture Degree of Graphs
No Thumbnail Available
Date
2016
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The rupture degree of a graph is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the weak version of the parameter. The weak-rupture degree of a connected graph G is defined to be R(G) = max{ (G-S)-| S |-me(G-S): S V (G),(G-S) > 1 } where(G-S) is the number of the components of (G-S) and me(G-S) is the number of edges of the largest component of G-S. Like the rupture degree itself, this is a measure of the vulnerability of a graph, but it is more sensitive. This paper, the weak-rupture degree of some special graphs are obtained and some bounds of the weak-rupture degree are given. Moreover some results about the weak-rupture degree of graphs obtained by graph operations are given. © 2016 World Scientific Publishing Company.