The super edge connectivity of kronecker product graphs

Let G 1 and G 2 be two graphs. The Kronecker product G 1 ×G 2 has vertex set V (G 1 ×G 2 ) = V (G 1 ) × V (G 2 ) and edge set E(G 1 × G 2 ) = f(u 1 ; v1)(u 2 ; v2) : U 1 u 2 ? E(G 1 ) and v1v2 ? E(G 2 )g. In this paper we determine the super edge-connectivity of G× Kn for n ?3. More precisely, for n ? 3, if ?0(G) denotes the super edge-connectivity of G, then at least minfn(n-1) ?0(G); minxy?E(G)fdegG(x) +degG(y)g(n-1)-2g edges need to be removed from G× Kn to get a disconnected graph that contains no isolated vertices. © EDP Sciences, ROADEF, SMAI 2018