HARMONIOUS LABELING OF SYMMETRICAL TREES OF DIAMETER FOUR
DEBDAS MISHRA
Department of Mathematics, C.V. Raman College of Engineering, Bhubaneswar, 752054 Odisha, India.
AMARESH CHANDRA PANDA *
Department of Mathematics, C.V. Raman College of Engineering, Bhubaneswar, 752054 Odisha, India.
*Author to whom correspondence should be addressed.
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 = b(modk).In this paper we prove that the symmetrical trees of diameter four admit harmonious labeling.
Keywords: Harmonious labeling, Symmetrical tree of diameter four.