The super edge connectivity of Kronecker product graphs

Abstract

Let G1 and G2 be two graphs. The Kronecker product G1 × G2 has vertex set V (G1 × G2) = V (G1) × V (G2) and edge set E(G1 × G2) = {(u1, v1)(u2, v2) : u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}. In this paper we determine the super edge–connectivity of G × Kn for n ≥ 3. More precisely, for n ≥ 3, if λ′(G) denotes the super edge–connectivity of G, then at least min{n(n-1)λ′(G), minxy∈E(G){degG(x)+degG(y)}(n-1)-2} edges need to be removed from G × Kn to get a disconnected graph that contains no isolated vertices.