MEAN RUPTURE DEGREE OF GRAPHS

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 p(1), p(2), ..., p(k), then m(G-S) = Sigma(k)(i=1)p(i)(2)/Sigma(k)(i=1)p(i). Formally, the mean rupture degree of a graph G, denoted mr(G), is defined as mr(G)= max{omega(G-S)-vertical bar S vertical bar-m(G-S): S subset of V(G), omega(G-S)>1} where omega(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.