Graph operations and neighbor-integrity

Abstract: Let $G$ be a graph. A vertex subversion strategy of $G$, 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-Integrity of $G$, $\NI(G)$, is defined to be $\NI(G) = \min_{S\subseteq V(G)} \{|S|+c(G/S)\}$, where $S$ is any vertex subversion strategy of $G$, and $c(G/S)$ is the maximum order of the components of $G/S$. In this paper we give some results connecting the neighbor-integrity and binary graph operations.

Keywords: vulnerability, integrity, neighbor-integrity

Classification (MSC2000): 05C40, 05C85

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