The harmonious coloring number of a graph

AbstractHopcroft and Krishnamoorthy (1983) have shown that the harmonious coloring problem is NP-complete, introducing the notion of a harmonious coloring of a graph as being a vertex coloring for which no two edges receive the same color-pair. In this report we construct efficient harmonious colorings of complete binary trees, 2 and 3-dimensional grids, and n-dimensional cubes