Vertex-neighbor-integrity of composition graphs of cycles

Abstract

Let X be a vertex set of a graph G. X is called a vertex subversion strategy of G if all the vertices in the closed neighborhood of X are removed from G. The survival subgraph is denoted by G/X. The vertexneighbor-integrity of G is defined as VNI(G) = min{|X| + Ι(G/X) : X C V(G)), where X is any vertex subversion strategy of G, Ι(G/X) is the order of a maximum component of G/X. This graph parameter was introduced by Cozzens and Wu to measure the vulnerability of a spy network. In this paper, the vertex-neighbor-integrity of the composition graph of two cycles is determined.