Vertex vulnerability parameters of Kronecker products of complete graphs

Let G(1) and G(2) be two graphs. The Kronecker product G(1) x G(2) of G(1) and 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 some vertex vulnerability parameters of the Kronecker product of complete graphs K-m x K-n for n >= m >= 2 and n >= 3. (C) 2007 Elsevier B.V. All rights reserved.