Study on Harmonious Labeling of Symmetrical Trees of Diameter Four

Abstract

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\(\cong\)b(modk).In this paper we prove that the symmetrical trees of diameter four admit harmonious labeling. Harmonious graphs can be used in the study of error correcting codes and channel assignment problems.