A note on the connectivity of direct products of graphs

Abstract

In recent years, the vertex connectivity and edge connectivity have aroused great interest of many scholars in the field of mathematics. We consider in this note that edge connectivity of a graph called k ′(G). In this note, If G is a bipartite graph with vertices n ≥ 3 we prove that k ′(G × K_n) = min {n(n – 1) k ′(G), (n – 1) δ(G)}, and their edge connectivity is satisfied k ′(G) = δ(G), we can obtain k ′(G × K_n) = δ (G × K_n) = (n – 1) δ(G).

Keywords:

• Edge connectivity
• Bipartite graph
• Edge-separating set
• Diret product