HARMONIOUS LABELING OF SYMMETRICAL TREES OF DIAMETER FOUR

A harmonious labeling on a graph G is an injection from the vertices of G to the group of integers modulo k , where k is the number of edges of G, that induces a bijection between the edges of G and the numbers modulo k by taking the edge label for an edge ab to be the sum of the labels of
the two vertices a = b(modk).In this paper we prove that the symmetrical trees of diameter four admit harmonious labeling.