Lucky Edge Labeling of H Graph, N Copies of H-Graph, Theta Graph, Duplication of Theta Graphs and Path Union of Theta Graphs

Abstract

In this paper, it is proved that the H-graphs, n copies of  H-graphs, Theta graph, Path union of Theta graph and Duplication of Theta graph are Lucky edge graphs.

Let G be a simple graph with vertex set edge set  respectively. Vertex set  and edge set  by positive integer and  denote the edge label such that it is the sum of labels of vertices incident with edge. The labeling is said to be lucky edge labeling, if the edge set  is a proper coloring of G that is if we have  wherever  are adjacent edges.