Equitable edge coloring on tensor product of graphs

Year 2020, Volume: 69 Issue: 2, 1336 - 1344, 31.12.2020

Vivik J Veninstine , M. M. Akbar Alı G. Gırıja

https://doi.org/10.31801/cfsuasmas.716392

https://izlik.org/JA57ZA86SS

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 $K_{1,m} \otimes K_{1,n}$.

Keywords

Equitable edge coloring , , Tensor product

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