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On the (pseudo) super edge-magic of 2-regular graphs and related graphs.
- Source :
- AIP Conference Proceedings; 2020, Vol. 2329 Issue 1, p1-7, 7p
- Publication Year :
- 2020
-
Abstract
- 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 edge xy ∈ 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 C<subscript>3</subscript> ∪ C<subscript>n</subscript> ∪ K<subscript>1</subscript> 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- GRAPH labelings
BIJECTIONS
INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 2329
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 148966660
- Full Text :
- https://doi.org/10.1063/5.0042216