A note on the connectivity of direct products of graphs. (18th August 2018) - Zhihui, Ma
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 × Kn ) = 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 × Kn ) = δ ( G × Kn ) = ( n – 1) δ ( G ).