Antimagicness of graphs with a dominating clique
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917157410963456 |
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| author | Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe |
| author_facet | Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe |
| contents | A graph $G = (V, E)$ is called antimagic if there exists a bijective labelling $f : E \rightarrow \{1, 2, \ldots, |E|\}$ such that the vertex-sums of labels over edges incident to a given vertex are all distinct. In this paper, we extend the antimagicness results over graphs with a dominating clique. We also introduce an alternative to the usual definition of antimagic graphs, called C-antimagic, allowing for the labelling to be injective in $\{1, 2, . . . , |E| + C\}$ instead of bijective, and show that almost all graphs with a dominating clique are 3-antimagic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Antimagicness of graphs with a dominating clique Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe Combinatorics A graph $G = (V, E)$ is called antimagic if there exists a bijective labelling $f : E \rightarrow \{1, 2, \ldots, |E|\}$ such that the vertex-sums of labels over edges incident to a given vertex are all distinct. In this paper, we extend the antimagicness results over graphs with a dominating clique. We also introduce an alternative to the usual definition of antimagic graphs, called C-antimagic, allowing for the labelling to be injective in $\{1, 2, . . . , |E| + C\}$ instead of bijective, and show that almost all graphs with a dominating clique are 3-antimagic. |
| title | Antimagicness of graphs with a dominating clique |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.17693 |