The harmonious chromatic number of a complete binary and trinary tree
The harmonious chromatic number of a graph \(G\), denoted by \(h(G)\), is the least number of colors which can be assigned to the vertices of \(G\) such that adjacent vertices are colored differently and any two distinct edges have different color pairs. This paper improves J. Mitchem's result [Discrete Math. 74, No. 1/2, 151-157 (1989; Zbl 0681.05030)] on the harmonious chromatic number of a complete binary tree and discusses the same problem for a complete trinary tree.
scientific article; zbMATH DE number 417453