On SD-prime labeling of graphs

Let G = (V(G),E(G)) be a simple, finite and undirected graph of order n. Given a bijection f : V(G) -→ {l,...,n}, and every edge uv in E(G)} one can associate two integers S = f(u) + f(v) and D = f(u) - f(v). The labeling f induces an edge labeling f : - {0,1} such that for an edge uv in E(G), f'(uv) = f if gcd(SiD) = 1, and f'(uv) - 0 otherwise. Such a labeling is called an SD-prime labeling if f'(uv) = 1 for all uv € E(G). We say G is SD-prime if it admits an SD-prime labeling. A graph G is said to be a strongly SD-prime graph if for every vertex v of G) there exists an SD-prime labeling f satisfying f(v) = 1. We investigate several results on this newly defined concept. In particular, we give a necessary and sufficient condition for the existence of an SD-prime labeling.