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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.11663 |
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| _version_ | 1866911783354105856 |
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| author | Latchoumanane, Vinothkumar Varadhan, Murugan Semaničová-Feňovčíková, Andrea |
| author_facet | Latchoumanane, Vinothkumar Varadhan, Murugan Semaničová-Feňovčíková, Andrea |
| contents | A graph $G$ is antimagic if there exists a bijection $f$ from $E(G)$ to $\left\{1,2, \dots,|E(G)|\right\}$ such that the vertex sums for all vertices of $G$ are distinct, where the vertex sum is defined as the sum of the labels of all incident edges. Hartsfield and Ringel conjectured that every connected graph other than $K_2$ admits an antimagic labeling. It is still a challenging problem to address antimagicness in the case of disconnected graphs. In this paper, we study antimagicness for the disconnected graph that is constructed as the direct product of a star and a path. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11663 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The direct product of a star and a path is antimagic Latchoumanane, Vinothkumar Varadhan, Murugan Semaničová-Feňovčíková, Andrea Combinatorics A graph $G$ is antimagic if there exists a bijection $f$ from $E(G)$ to $\left\{1,2, \dots,|E(G)|\right\}$ such that the vertex sums for all vertices of $G$ are distinct, where the vertex sum is defined as the sum of the labels of all incident edges. Hartsfield and Ringel conjectured that every connected graph other than $K_2$ admits an antimagic labeling. It is still a challenging problem to address antimagicness in the case of disconnected graphs. In this paper, we study antimagicness for the disconnected graph that is constructed as the direct product of a star and a path. |
| title | The direct product of a star and a path is antimagic |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2308.11663 |