Neighbor Rupture Degree of Transformation Graphs Gxy-

A vulnerability parameter the neighbor rupture degree can be used to obtain the vulnerability of a spy network. The neighbor rupture degree of a noncomplete connected graph G is defined to be Nr(G) = max{w(G/S) - |S| - 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. In this study, the neighbor rupture degree of transformation graphs of path graphs, cycle graphs, wheel graphs, complete graphs and complete bipartite graphs are obtained.