The exact value of the harmonious chromatic number of a complete binary tree Original Research Article

The harmonious chromatic number of a graph G, denoted by h(G), is the least number of colors needed to color the vertices of G in such a way that adjacent vertices are colored by different colors and any two distinct edges receive different color pairs. D. Johnson has shown that the problem of determining h(G) is NP-hard. In this paper, we determine the exact value of the harmonious chromatic number of a complete binary tree.