Skolem difference mean graphs

Abstract

A graph G = (V, E) with p vertices and q edges is said to have skolem difference mean labeling if it is possible to label the vertices x ∈ V with distinct elements f (x) from 1, 2, 3, · · · , p+q in such a way that for each edge e = uv, let f*(e)= ⌈|f(u)-f(v)|/2⌉ and the resulting labels of the edges are distinct and are from 1, 2, 3, · · ·, q. A graph that admits a skolem difference mean labeling is called a skolem difference mean graph. In this paper, we prove Cn@Pm(n ≥ 3, m ≥ 1), are skolem difference mean graphs.