A Performance on Harmonious Coloring of Barbell Graph

Abstract

Given simple graph 𝑮, a harmonious chromatic number 𝝌𝒉(𝑮) is the minimum number of colors used in a graph such that no two adjacent vertices receives the same color and each combination of color seems together on atmost one edge. In this article we have determined the harmonious chromatic number of barbell and central graph of barbell graph.Over all we have given an algorithm to calculate the harmonious chromatic number of Barbell graph by depicting a quadratic time.