Equitable edge coloring on tensor product of graphs

Abstract

A graph G is edge colored if different colors are assigned to its edges or lines, in the order of neighboring edges are allotted with least diverse k-colors. If each of k-colors can be partitioned into color sets and differs by utmost one, then it is equitable. The minimum of k-colors required is known as equitably edge chromatic number and symbolized by $\chi^{\prime}_{=}(G)$. Further the impression of equitable edge coloring was first initiated by Hilton and de Werra in 1994. In this paper, we ascertain the equitable edge chromatic number of $P_m \otimes P_n$, $P_m \otimes C_n$ and $K_{1,m} \otimes K_{1,n}$.