A vertex subversion strategy of a graph G is a set of vertices X subset of V(G) whose closed neighborhood is deleted from G. The survival subgraph is denoted by G/X. The vertex-neighbor-integrity of G is defined to be VNI(G) = min {vertical bar X vertical bar + tau(G/X) : X subset of V(G)} where tau(G/X) is the order of a largest component in G/X. This graph parameter was introduced by Cozzens and Wu to measure the vulnerability of spy networks. It was proved by Gambrell that the decision problem of computing the vertex-neighbor-integrity of a graph is NP-complete. In this paper we evaluate the vertex-neighbor-integrity of the composition graph of two paths.
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