On b-edge consecutive edge magic total labeling on trees

Eunike Setiawan (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, , Indonesia)
Kiki Ariyanti Sugeng (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia)
Denny Riama Silaban (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications

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.