On equitable coloring of book graph families

Year 2020, Volume: 69 Issue: 2, 1228 - 1234, 31.12.2020

M. Baranı Venkatachalam M , K. Rajalakshmı

https://doi.org/10.31801/cfsuasmas.769094

https://izlik.org/JA37SP74RD

Abstract

A proper vertex coloring of a graph is equitable if the sizes of color classes differ by atmost one. The notion of equitable coloring was introduced by Meyer in 1973. A proper $h-$colorable graph $K$ is said to be equitably h-colorable if the vertex sets of $K$ can be partioned into $h$ independent color classes $V_1, V_2,...,V_h$ such that the condition $\left|\left|V_i\right|-\left|V_j\right|\right| \leq 1$ holds for all different pairs of $i$ and $j$ and the least integer $h$ is known as equitable chromatic number of $K$. In this paper, we find the equitable coloring of book graph, middle, line and central graphs of book graph.

Keywords

equitable coloring , book graph , middle graph , line graph , central graph

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