TY - GEN
T1 - On the (Pseudo) Super Edge-Magic of 2-Regular Graphs and Related Graphs
AU - Krisnawati, Vira Hari
AU - Ngurah, Anak Agung Gede
AU - Hidayat, Noor
AU - Alghofari, Abdul Rouf
N1 - Publisher Copyright:
© 2021 American Institute of Physics Inc.. All rights reserved.
PY - 2021/2/26
Y1 - 2021/2/26
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85102512133
U2 - 10.1063/5.0042216
DO - 10.1063/5.0042216
M3 - Conference contribution
AN - SCOPUS:85102512133
T3 - AIP Conference Proceedings
BT - International Conference on Mathematics, Computational Sciences and Statistics 2020
A2 - Alfiniyah, Cicik
A2 - Fatmawati, null
A2 - Windarto, null
PB - American Institute of Physics Inc.
T2 - International Conference on Mathematics, Computational Sciences and Statistics 2020, ICoMCoS 2020
Y2 - 29 September 2020
ER -