Graph Operations and Neighbor Rupture Degree

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 graphG, say S, is a set of vertices inGwhose 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)−|S|−c(G/S) : S ⊂ V(G), w(G/S) ≥ 1}, where S is any vertex subversion strategy ofG,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.