Edge-Tenacity

The edge-tenacity $T_e(G)$ of a graph G was defined asbegin{center} $T_e(G)=displaystyle min_{Fsubset E(G)}{frac{mid Fmid +tau(G-F)}{omega(G-F)}}$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 $Fsubset E(G)$ is said to be a $T_e$-set of G ifbegin{center} $T_e(G)=frac{mid Fmid+tau(G-F)}{omega(G-F)}$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.