Integer-antimagic spectra of tadpole and lollipop graphs
Wai Chee Shiu, Pak Kiu Sun, M. Richard Low · HKBU Institutional Repository (Hong Kong Baptist University) · 2015
Let $A$ be a non-trival abelian group. A connected 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 article, we determine the integer-antimagic spectra of tadpole and lollipop graphs.