The edge tenacity of a split graph

The edge tenacity Te(G) of a graph G is dened as: Te(G) = minfjXj+(G-X) !(G-X)􀀀1 jX E(G) and !(G - X) > 1g where the minimum is taken over every edge-cutset X that separates G into !(G 􀀀 X) components, and by (G􀀀X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I;E) be a noncomplete connected split graph with minimum vertex degree (G) we prove that if (G) jE(G)j jV (G)j􀀀1 then its edge-tenacity is jE(G)j jV (G)j􀀀1 .