Vira Hari Krisnawati, Anak Agung Gede Ngurah, Noor Hidayat, Abdul Rouf Alghofari
Let G =(V, E) be finite and simple graphs with vertex set V(G) and edge set E(G). A graph G is called super edge-magic if there exists a bijection f: V(G) ≊ E(G) → {1, 2, ⋯, |V(G)| + |E(G)|} and f(V(G)) = {1, 2, ⋯, |V(G)|} such that f(x) + f(xy) + f(y) is a constant for every edgexy ∈ E(G). A graph G with isolated vertices is called pseudo super edge-magic if there exists a bijection f: V(G) → {1, 2, ⋯, |V(G)|} such that the set {f(x) + f(y) : Xy ∈ E(G)} ≊ {2f(x) : Deg(x) = 0} consist of |E(G)| + |{x ∈ V(G) : Deg(x) = 0}| consecutive integers. In this paper, we construct (pseudo) super edge-magic 2-regular graphs from a super edge-magic cycle by using normalized Kotzig arrays. We also show that the graph C3 ≊ Cn ≊ K1 is pseudo super edge-magic for n ≡ 1(mod 4). By this result, we obtain some new classes of super edge-magic 2-regular graphs. In addition, we show that union of cycles and paths are super edge-magic. © 2021 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Faculty of Sciences, University of Brawijaya, Jl. Veteran Malang, East Java, Indonesia; Department of Civil Engineering, Faculty of Engineering, Universitas Merdeka, Jl. Taman Agung No. 1 Malang, East Java, Indonesia
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