Further results on SD-prime labeling

Let G = (V(G),E(G)) be a simple, finite and undirected graph with n vertices. Given a bijection f : V(G) → {1,., n}, one can associate two integers S = f(u) + f(v) and D = f(u) - f(v)| with every edge uv ϵ E(G). The labeling / induces an edge labeling f : E(G) → {0,1} such that for any edge uv in E(G), f′{uv) = 1 if gcd(S, D) = 1, and f′(uv) = 0 otherwise. Such a labeling is called an SD-prime labeling if gcd = 1 for all uv ∈. (G). We say that 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-prirae labeling f satisfying f(ν) = 1. In this paper, we first give some sufficient conditions for a theta graph to be strongly SD-prime. We then give constructions of new SD-prime graphs from known SD-prime graphs and investigate the SD-primality of some general graphs.