On b-edge consecutive edge magic total labeling on trees

Abstract

Let G = ( V , E ) be a simple, connected, and undirected graph, where V and E are the set of vertices and the set of edges of G . An edge magic total labeling on G is a bijection f : V ∪ E → {1, 2, …, | V |+| E |} , provided that for every u v ∈ E , w ( u v )= f ( u )+ f ( v )+ f ( u v )= K for a constant number K . Such a labeling is said to be a super edge magic total labeling if f ( V )={1,2,…,| V |} and a b -edge consecutive edge magic total labeling if f ( E )={ b +1, b +2,…, b +| E |} with b ≥ 1 . In this research, we give sufficient conditions for a graph G having a super edge magic total labeling to have a b -edge consecutive edge magic total labeling. We also give several classes of connected graphs which have both labelings.