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 f: V → E → {1, 2, ..., |V | + |E|}, provided that for every uv ∈ E,w(uv) = f(u) + f(v) + f(uv) = 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. [ABSTRACT FROM AUTHOR]