On b-edge consecutive edge magic total labeling on trees

Eunike Setiawan, Kiki Ariyanti Sugeng, Denny Riama Silaban

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 : 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.

Keywords


super edge magic total labeling; $b$-edge consecutive edge magic total labeling; tree graph

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DOI: http://dx.doi.org/10.5614/ejgta.2022.10.2.15

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