The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs - Ugur Odabasi; Dan Roberts; Richard M. Low (Theory and Applications of Graphs)
A simple graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is \emph{$\mathbb{Z}_{k}$-antimagic} if there exists a function $f: E(G) → \mathbb{Z}_{k} \backslash \{0\}$ such that the induced function $f^+(v)=\sum_{uv\in E(G)} f(uv)$ is injective. The integer-antimagic spectrum of a graph $G$ is the set IAM$(G) = \{k: G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic and } k ≥ 2\}$. A weak join of vertex-disjoint graphs is the collection of the graphs with additional simple edges (possibly none) between the original graphs. In this paper, we characterize IAM$(H)$ where $H$ is a weak join of Hamiltonian graphs.