On equitable coloring of book graph families

Authors : M. BARANI, Venkatachalam M, K. RAJALAKSHMI

Pages : 1228-1234

Doi:10.31801/cfsuasmas.769094

View : 7 | Download : 7

Publication Date : 2020-12-31

Article Type : Research Paper

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