Edge-Tenacity

The edge-tenacity Te(G) of a graph G was dened as Te(G) = min FE(G) f j F j + (G 􀀀 F) !(G 􀀀 F) g where the minimum is taken over all edge cutset F of G. We dene G-F to be the graph induced by the edges of E(G)􀀀F, (G􀀀F) is the number of edges in the largest component of the graph induced by G-F and !(G 􀀀 F) is the number of components of G􀀀F. A set F E(G) is said to be a Te-set of G if Te(G) = jFj+(G􀀀F) !(G􀀀F) Each component has at least one edge. In this paper we introduce a new invariant edge-tenacity, for graphs. it is another vulnerability measure. we present several properties and bounds on the edge-tenacity. we also compute the edge-tenacity of some classes of graphs.