Harmonious Coloring on Corona Product of Complete Graphs

Abstract

In this paper, we find the harmonious chromatic number of the corona product of any graph G of order l with the complete graph K n for l n. As a consequence of this work, we also obtain the harmonious chromatic number of t copies of K n for t n þ 1.

Remarks on Fractional Locally Harmonious Coloring

“…Edwards [12] gave an upper bound for the harmonious chromatic number of a general directed graph, and showed that determining the exact value of the harmonious chromatic number is NP-hard for directed graphs of bounded degree. Muntaner-Batle et al [13] found the harmonious chromatic number of the corona product of any graph G of order l with the complete graph K n for l ≤ n. As a consequence of this work, then also obtained the harmonious chromatic number of t copies of K n for t ≤ n + 1. Hegde and Castelino [14] investigated the proper harmonious coloring number of graphs such as unidirectional paths, unicycles, inspoken and outspoken wheels, n-ary trees of different levels etc.…”