Mean rupture degree of graphs

ASLAN E., BACAK TURAN G.

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, vol.78, no.1, pp.233-242, 2016 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 78 Issue: 1
  • Publication Date: 2016
  • Journal Name: UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.233-242
  • Keywords: Connectivity, Graph theory, Integrity, Mean integrity, Rupture degree
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

The vulnerability shows the resistance of the network until communication breakdown after the disruption of certain stations or communication links. We introduce a new graph parameter, the mean rupture degree. Let G be a graph of order p and S be a subset of V(G). The graph G-S contains at least two components and if each one of the components of G-S have orders p1, p2,pk, then m(G-S)=Σtk=pi2/Σtk=pt Formally, the mean rupture degree of a graph G, denoted mr(G), is defined as mr(G)=max-ω(G-S)-|S|- (G-S): SV(G), ω(G-S)1} where ω(G-S) denote the number of components. In this paper, the mean rupture degree of some classes of graphs are obtained and the relations between mean rupture degree and other parameters are determined.