On the Harmonious Coloring of Certain Class of Graphs

By : V. Sriram, Medha Itagi Huilgol

Page No: 17-29

Abstract
Given a simple graph G a harmonious coloring of G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number is the least integer k for which G admits a harmonious coloring with k colors. In this paper the harmonious chromatic number of distance degree regular graphs of diameter 3 is given. In this paper we also provide the harmonious chromatic number of some class of graphs viz., Parachute graph, Gear graph, Hn,n, Helm graph, Jelly fish. If G is a simple graph with n vertices, we give a constructive technique to harmoniously color G  K ? mi , for 1 ? i ? n given that the graph G with n vertices has harmonious chromatic number k.

Authors :
Medha Itagi Huilgol and V. Sriram : Department of Mathematics, Bangalore University, Bengaluru, India.