Vertex Magic Total Labeling Of Generalized Petersen Graphs

Abstract

Let G = (V,E) be a simple and finite graph with a vertex – set V and an adge – set E. A vertex-magic total labeling of a graph G is a bijective mapping from V  E to {1, 2, 3, …, h} such that for each vertex x in Graph G satisfying λx+λ(xy)= k, where the sum is over all vertices y adjacent to x, for a constant k. Then k named a magic constant and G named vertex-magic total graph. In this paper we consider a vertex-magic labeling of generalized Petersen graph. The main focus is modeling of vertex-magic total labeling generalized Petersen graph and two copies of generalized Petersen graphs with a constant k.