Fibonacci Harmonious Graph of a Group

Abstract

Consider the commutative group G. Fibonacci Harmonious labeling is a novel labeling system that we introduce. If the vertices of a graph G with m edges can be labeled with different integers from the set {0, 1, 2, …, } the derived edge labels are the Fibonacci numbers, then the graph is Fibonacci Harmonious graph. We demonstrate this Friendship graphs, Fan graph, Star graph, Jelly Fish graph, Comb graph are Fibonacci Harmonious graph. The result of a study of the Fibonacci Harmonious graph and its generalizations on Group are presented in this work.