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 :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.