Reverse super edge-magic strength of some new classes of graphs

Abstract

In this paper, we introduce new concepts of reverse super edge-magic labeling and reverse super edge-magic strength of a graph G. A graph G is said to be reverse super edge-magic if there exists a bijection f : V ⋃ E → {1,2, …, p + q}, such that f (uv) – [f (u) + f (v)] is a constant, for all uv ∈ E and f (V) = {1,2,…, p}. Such a bijection is called a reverse super edge-magic labeling and the minimum of all constants is called a reverse super edge-magic strength of the graph G, where the minimum is taken over all reverse super edge-magic labelings of G. Also we obtain the reverse super edge-magic labelings and reverse super edge-magic strength of some well known graphs such as the y-tree Yn, the cycle C 2n+1, the generalized Petersen graph P(m, k) and the disconnected graph (2m + 1)C 3.