Tenacity of a graph with maximum connectivity

Abstract

The tenacity of a graph $G$, $T\left(G\right)$, is defined by $T\left(G\right)=min\left\{\frac{\left|S\right|+\tau (G-S)}{\omega (G-S)}\right\}$, where the minimum is taken over all vertex cutsets $S$ of $V\left(G\right)$, $\omega (G-S)$ is the number of components of $G-S$ and $\tau (G-S)$ is the number of vertices in the largest component of the graph induced by $G-S$.

In this paper we choose the spectrum of a graph, $G_n^m$, which is $n$-vertex-connected with minimum number of edges and we calculate the tenacity of $G_n^m$.