On the Edge-Tenacity of Graphs
نویسندگان
چکیده
The edge-tenacity Te(G) of a graph G was defined as Te(G) = min F⊂E(G) {| F | +τ(G− F ) ω(G− F ) } where the minimum is taken over all edge cutset F of G. We define G-F to be the graph induced by the edges of E(G) − F , τ(G − F ) is the number of edges in the largest component of the graph induced by G-F and ω(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) = |F |+τ(G−F ) ω(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. 930 D. Moazzami and B. Salehian
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