Find in Library

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.