Graph Operations and Neighbor Rupture Degree

Abstract

In a communication network the vulnerability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. A vertex subversion strategy of a graph G say S is a set of vertices in G whose closed neighborhood is removed from G. The survival subgraph is denoted by G/S. The neighbor rupture degree of G Nr(G) is defined to be Nr(G) = max{w(G/S) - vertical bar S vertical bar - c(G/S) : S subset of V(G) w(G/S) > 1} where S is any vertex subversion strategy of G w(G/S) is the number of connected components in G/S and c(G/S) is the maximum order of the components of G/S (G. Bacak Turan 2010). In this paper we give some results for the neighbor rupture degree of the graphs obtained by some graph operations.