Reverse super edge-magic strength of banana trees

摘要

A reverse magic labelling of a graph G(V, E) is a bijection f : V ∪ E → {1, 2, 3, ......, v + ε } 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 + ε }. 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.