On odd prime labeling of graphs

In this paper we give a new variation of the prime labeling. We call a graph G with vertex set V ( G ) has an odd prime labeling if its vertices can be labeled distinctly from the set { 1 , 3 , 5 , … , 2 ∣ ∣ V ( G ) ∣ ∣ − 1 } such that for every edge x y of E ( G ) the labels assigned to the vertices of x and y are relatively prime. A graph that admits an odd prime labeling is called an odd prime graph. We give some families of odd prime graphs and give some necessary conditions for a graph to be odd prime. Finally, we conjecture that every prime graph is odd prime graph.