Locally Harmonious Chromatic Number of Certain Tree-Structured Networks

Abstract

Graph coloring is one of the oldest and best-known problems of graph theory. The locally harmonious coloring of G is a proper vertex coloring in which adjacent edges receive different color pairs [3]. In another way, all the vertices in N [v] receive different colors for all v in G. The minimum number of colors required to obtain a locally harmonious coloring of a graph G is called the locally harmonious chromatic number of G and is denoted by h1(G). In this paper, we investigate the locally harmonious chromatic number of slim tree, hypertree, shuffle hypertree and l-complete binary tree.