The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs

Authors

Ugur Odabasi, Istanbul University-CerrahpasaFollow
Dan Roberts, Illinois Wesleyan UniversityFollow
Richard M. Low, San Jose State UniversityFollow

Abstract

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 $f: E(G) \to \mathbb{Z}_{k} \backslash \{0\}$ such that the induced function $f^+(v)=\sum_{uv\in E(G)} f(uv)$ is injective. The \textit{integer-antimagic spectrum} of a graph $G$ is the set IAM$(G) = \{k: G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic and } k \geq 2\}$. A \emph{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.

Creative Commons License

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Recommended Citation

Odabasi, Ugur; Roberts, Dan; and Low, Richard M. (2025) "The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs," Theory and Applications of Graphs: Vol. 12: Iss. 1, Article 5.
DOI: 10.20429/tag.2025.120105
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol12/iss1/5