THE SUPER EDGE CONNECTIVITY OF KRONECKER PRODUCT GRAPHS

摘要

Let G(1) and G(2 )be two graphs. The Kronecker product G(1) x G(2) has vertex set V(G(1) x G(2)) = V(G(1)) x V(G(2)) and edge set E(G(1) x G(2)) = { (u(1), v(1)) (u(2) , v(2)) : u(1)u(2) is an element of E(G(1)) and v(1)v(2) is an element of E(G(2)) }. In this paper we determine the super edge-connectivity of G x K-n for n = 3. More precisely, for n = 3, if lambda' (G) denotes the super edge-connectivity of G, then at least min{ n(n - 1) lambda' (G), min(xy)(is an element of E(G)) { deg(G)(x) +deg(G) (y)}(n -1) - 2 } edges need to be removed from G x K-n to get a disconnected graph that contains no isolated vertices.