Reverse Super Edge-Magic Labelings of P_2C_n and W_o (2,n)

Abstract

A graph G = (V(G),E(G))  with  |V(G)| = p and |E(G)| = q , is called reverse super edge-magic if there exists a bijection f from V(G)UE(G) onto {1, 2, 3…, p + q} and a constant c^{-1}(f) such that c^{-1}(f) = f(uv)-(f(u)+f(v)) for all uv \in E(G) and f(V(G))={1,2,3,…,p} . This bijection f is called a reverse super edge-magic labeling for G and the minimum of all constants c^{-1}(f) taken over all reverse super edge-magic labeling of G is called the reverse super edge-magic strength of G and denoted by rsems(G). This article constructs reverse super edge-magic labelings for P_2 ? C_n and W_o (2,n) for an odd integer n such that n >= 3  and prove that rsem(P_2 ? C_n) = (3n-1)/2 and (5n-2)/4 <= rsem(W_o (2,n)) <= (5n-1)/2  for an odd integer n such that n >= 3.