Weak-Rupture Degree of Graphs

ASLAN E.

International Journal of Foundations of Computer Science, vol.27, no.6, pp.725-738, 2016 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.1142/s0129054116500258
  • Journal Name: International Journal of Foundations of Computer Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.725-738
  • Keywords: connectivity, graph theory, Network design and communication, rupture degree, weak integrity
  • Manisa Celal Bayar University Affiliated: Yes

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.