b - Bonacci Harmonious Graph on Finite Group
Abstract
Consider the commutative group G. We introduce a novel labeling system called b-Bonacci Harmonious labeling. 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 b-Bonacci numbers. Then that graph is called b-Bonacci Harmonious graph. We demonstrate whether this are Fan graph, Bistar graph, Jelly Fish graph, Comb graph, Star graph, [ graph and Path graph are b-Bonacci Harmonious graph.The result of a study of the b-Bonacci Harmonious graph and its generalizations on Group are presented in this work.