The Integer-antimagic Spectra of a Weak Join of Hamiltonian 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 $f: E(G) \to \mathbb{Z}_{k} \backslash \{0\}$ such that the induced function $f^+(v)=\sum_{uv\in E(G)} f(uv)$ is injective. The \textit{integer-antimagic spectrum} of a graph...
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Georgia Southern University
2025-05-01
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| Series: | Theory and Applications of Graphs |
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| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol12/iss1/5/ |
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| author | Ugur Odabasi Dan Roberts Richard M. Low |
| author_facet | Ugur Odabasi Dan Roberts Richard M. Low |
| author_sort | Ugur Odabasi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2015e6c86bd647fdaaffe47c6597a7d8 |
| institution | OA Journals |
| issn | 2470-9859 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Georgia Southern University |
| record_format | Article |
| series | Theory and Applications of Graphs |
| spelling | doaj-art-2015e6c86bd647fdaaffe47c6597a7d82025-08-20T02:38:10ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592025-05-0112110.20429/tag.2025.120105The Integer-antimagic Spectra of a Weak Join of Hamiltonian GraphsUgur Odabasi Dan RobertsRichard M. Low 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.https://digitalcommons.georgiasouthern.edu/tag/vol12/iss1/5/integer-antimagicgraph labelinghamiltonian graph |
| spellingShingle | Ugur Odabasi Dan Roberts Richard M. Low The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs Theory and Applications of Graphs integer-antimagic graph labeling hamiltonian graph |
| title | The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs |
| title_full | The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs |
| title_fullStr | The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs |
| title_full_unstemmed | The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs |
| title_short | The Integer-antimagic Spectra of a Weak Join of Hamiltonian Graphs |
| title_sort | integer antimagic spectra of a weak join of hamiltonian graphs |
| topic | integer-antimagic graph labeling hamiltonian graph |
| url | https://digitalcommons.georgiasouthern.edu/tag/vol12/iss1/5/ |
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