Integer-antimagic spectra of disjoint unions of cycles

Authors

Wai Chee Shiu, Hong Kong Baptist UniversityFollow

Abstract

Let A be a non-trivial abelian group. A simple graph G = (V, E) is A-antimagic if there exists an edge labeling f: E(G) \to A \setminus \{0\} such that the induced vertex labeling f^+: V(G) \to A, defined by f^+(v) = \sum_{uv\in E(G)}f(uv), is injective. The integer-antimagic spectrum of a graph G is the set IAM(G) = \{k\;|\; G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic and } k \geq 2\}. In this paper, we determine the integer-antimagic spectra of disjoint unions of cycles.

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Recommended Citation

Shiu, Wai Chee (2018) "Integer-antimagic spectra of disjoint unions of cycles," Theory and Applications of Graphs: Vol. 5: Iss. 2, Article 3.
DOI: 10.20429/tag.2018.050203
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol5/iss2/3