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 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) -|s| - c(g/s): s ⊂ 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. © 2013 saadet kandilci et al.