Strongly Multiplicative Labeling of Some Butterfly Graphs

Abstract

A graph  (V, E) with p vertices and q edges called strongly multiplicative if the vertices of  can be labeled with p consecutive positive integers 1,2,…,p such that the label induced on the edges by the product of labels of end vertices are all distinct. In this manuscript we prove that the Generalized Butterfly Graph , Shell Butterfly Graph, Special Butterfly Graph  , and the Butterfly Graph of  are all strongly multiplicative.