On duplication of near Skolem difference mean graph Pn

Abstract

Let G be a (p,q) graph and f:V(G)→{1,2,…,p+q-1,p+q+2} be an injection. For each edge e=uv, the induced edge labeling f^* is defined as follows: Then f is called Near Skolem difference mean labeling if f^* (e) are all distinct and from {1,2,3,….q}. A graph that admits a Near Skolem difference mean labeling is called a Near Skolem difference mean graph. In this paper, we show that the graph obtained by duplicating a vertex or an edge in a Near Skolem Difference Mean graph P_n is also a Near skolem difference mean graph.