ON EQUITABLE COLORING OF BOOK GRAPH FAMILIES

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 V1, V2, ..., Vh such that the condition ††Vi† — †V(†† ≤ 1 holds for all dif- ferent pairs of i and ( 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.