Equitable Edge Coloring of a Prism and Generalized Petersen Graphs p(n,m) for any n and m=2,3

Abstract

An Equitable coloring of graph G is a proper k -coloring C that verifies the following property: for every color class ci , 1 ≤ i ≤ k, there exists a vertex xi , with color ci , such that all the other colors in C are utilized in xi neighbors. In this paper, we discussed the equitable coloring of the prisms and generalized Petersen graphs ????(????, ????),