Equitable Coloring And Connectivity Of Direct Products Of Some Graphs

The equitable chromatic number of some special graphs is considered in the first part of this paper.The lower bound on equitable chromatic thresholds of Kn,mn and Kl,m×Kn have been given. The exact value of equitable chromatic threshold of Kn,mn, for integers n≥2, m≥2 with n and m odd is shown in this paper. At the same time, the equitable chromatic number and equitable chromatic threshold of direct products of some special classes of graphs with a complete graph are considered in this paper. The latter part deals with the connectivity and edge connectivity of direct products. The connectivity of G×K2 has been given. In addition, we give edge connectivity and the structure of minimum edge cuts of G×H, forδ(H)>|V(H)|/2.