2023
DOI: 10.26637/mjm1103/004
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Integrity and vertex neighbor integrity of some graphs

Abstract: The integrity $I(G)$ of a noncomplete connected graph $G$ is a measure of network vulnerability and is defined by $I(G)=\min\limits_{S\subset V(G)}\{ |S|+m(G-S)\}$, where $S$ and $m(G-S)$ denote the subset of $V$ and the order of the largest component of $G-S$, respectively. The vertex neigbor integrity denoted as $VNI(G)$ is the concept of the integrity of a connected graph $G$ and is defined by $VNI(G)=\min\limits_{S\subset V(G)}\{|S|+m(G-S)\}$, where $S$ is any vertex subversion strategy of $G$ and $m(G-S)$… Show more

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