On b-edge consecutive edge magic total labeling on trees - Eunike Setiawan; Kiki Ariyanti Sugeng; Denny Riama Silaban (Electronic Journal of Graph Theory and Applications (EJGTA), 2022)
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.