.Dara Moazzami
Abstract
The edge-tenacity $T_e(G)$ of a graph G was defined as\begin{center} $T_e(G)=\displaystyle \min_{F\subset E(G)}\{\frac{\mid F\mid +\tau(G-F)}{\omega(G-F)}\}$\end{center}where the minimum is taken over all edge cutset F of G. We defineG-F to be the graph induced by the edges of $E(G)-F$, $\tau(G-F)$is ...
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The edge-tenacity $T_e(G)$ of a graph G was defined as\begin{center} $T_e(G)=\displaystyle \min_{F\subset E(G)}\{\frac{\mid F\mid +\tau(G-F)}{\omega(G-F)}\}$\end{center}where the minimum is taken over all edge cutset F of G. We defineG-F to be the graph induced by the edges of $E(G)-F$, $\tau(G-F)$is the number of edges in the largest component of the graphinduced by G-F and $\omega(G-F)$ is the number of components of$G-F$. A set $F\subset E(G)$ is said to be a $T_e$-set of G if\begin{center} $T_e(G)=\frac{\mid F\mid+\tau(G-F)}{\omega(G-F)}$\end{center}Each component has at least one edge. In this paper we introducea new invariant edge-tenacity, for graphs. it is another vulnerability measure.we present several properties and bounds on the edge-tenacity. we alsocompute the edge-tenacity of some classes of graphs.