Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs

Abstract

A finite, simple graph of order k is said to be a strongly multiplicative graph when all vertices of the graph are labeled by positive integers 1,2,3 , … , k such that the induced edge labels of the graph, obtained by the product of labels of end vertices of edges, are distinct. In this paper, we show that the diamond graph B r n for 𝑛 ≥ 3, umbrella graph U m , n , and generalized Petersen graph GP n , k , for n ≥ 3 and 1 ≤ k < n / 2 , admit strongly multiplicative labeling. Moreover, strongly multiplicative labeling of a double comb graph and sunflower planar graph has also been investigated and elaborated as well with different examples.