Reverse super edge-magic strength of banana trees

Abstract

A reverse magic labelling of a graph G(V, E) is a bijection f: V ∪ E → {1, 2, 3, ......, v + e} such that for all edges xy, f(xy) - {f(x) + f(y)} is a constant which is denoted by c(f). A reverse magic labelling of a graph G(V, E) is called reverse super edge-magic labelling of G if f(V) = {1, 2, ...... v} and f(E) = {v + 1, v + 2, ......, v + e}. The reverse super edge-magic strength of a graph G,rsm(G), is defined as the minimum of all c(f) where the minimum is taken over all reverse edge-magic labelling f of G. In this paper we invented the reverse super edge-magic strength of banana trees.