A note on the connectivity of Kronecker products of graphs

Let κ(G)κ(G) be the connectivity of GG. The Kronecker product G1×G2G1×G2 of graphs G1G1 and G2G2 has vertex set V(G1×G2)=V(G1)×V(G2)V(G1×G2)=V(G1)×V(G2) and edge set E(G1×G2)={(u1,v1)(u2,v2):u1u2∈E(G1) and v1v2∈E(G2)}E(G1×G2)={(u1,v1)(u2,v2):u1u2∈E(G1) and v1v2∈E(G2)}. In this paper, we prove that κ(G×Kn)=min{nκ(G),(n−1)δ(G)}κ(G×Kn)=min{nκ(G),(n−1)δ(G)}, where GG is a bipartite graph.