On (Semi-) Edge-primality of Graphs

Let G = (V, E) be a (p, q)-graph. A bijection f : E + {1,2,3,...,9} is called an edge-prime labeling if for each edge uv in E, we have GCD(f+(u), f+(u)) = 1 where f+(u) = {uwee f(uw). More over, a bijection f: E + {1,2,3,...,9} is called a semi-edge-prime la beling if for each edge uv in E, we have GC D(f+(u), ft(u)) = 1 or f+(u) = f+(v). A graph that admits an edge prime (or a semi-edge prime) labeling is called an edge prime (or a semi-edge-prime) graph. In this paper we determine the necessary and/or sufficient condition for the existence of (semi-) edge-primality of bipartite and tripartite graphs.