Graph operations and neighbor rupture degree (Q364548)

Summary: 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 \(G\), \(\text{Nr}(G)\), is defined to be \(\text{Nr}(G) = \max\{w(G/S) - |S| - c(G/S) : S \subset V(G), w(G/S) \geq 1\}\), 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.