Vertex-neighbour-integrity of composition graphs of paths and cycles

  • Authors:

  • Zongtian Wei;Shenggui Zhang

  • Affiliations:

  • Department of Mathematics, Xi'an University of Architecture and Technology, Xi'an, Shaanxi, P.R. China;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi, P.R. China

  • Venue:
  • International Journal of Computer Mathematics
  • Year:
  • 2008

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Abstract

A vertex subversion strategy of a graph G is a set of vertices X⊆ V(G) whose closed neighbourhood is deleted from G. The survival subgraph is denoted by G/X. The vertex-neighbour-integrity of G is defined to be VNI(G)=min{|X|+τ(G/X):X⊆ V(G)}, where τ(G/X) is the maximum order of the components of G/X. This graph parameter was introduced by Cozzens and Wu to measure the vulnerability of spy networks. Gambrell proved that the decision problem of computing the vertex-neighbour-integrity of a graph is NP-complete. In this paper we evaluate the vertex-neighbour-integrity of the composition graphs of paths and cycles.