On b-edge consecutive edge magic total labeling on trees

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 (Formula Presented) provided that for every (Formula Presented) for a constant number K. Such a labeling is said to be a super edge magic total labeling if (Formula Presented) and a b-edge consecutive edge magic total labeling if (Formula Presented). 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.