The number of distinguishing colorings of a Cartesian product graph
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866913226338336768 |
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| author | Alikhani, Saeid Shekarriz, Mohammad Hadi |
| author_facet | Alikhani, Saeid Shekarriz, Mohammad Hadi |
| contents | A vertex coloring is called distinguishing if the identity is the only automorphism that can preserve it. The distinguishing threshold $θ(G)$ of a graph $G$ is the minimum number of colors $k$ required that any arbitrary $k$-coloring of $G$ is distinguishing. In this paper, we calculate the distinguishing threshold of a Cartesian product graph. Moreover, we calculate the number of non-equivalent distinguishing colorings of grids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_00635 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The number of distinguishing colorings of a Cartesian product graph Alikhani, Saeid Shekarriz, Mohammad Hadi Combinatorics 05C09, 05C15, 05C76 A vertex coloring is called distinguishing if the identity is the only automorphism that can preserve it. The distinguishing threshold $θ(G)$ of a graph $G$ is the minimum number of colors $k$ required that any arbitrary $k$-coloring of $G$ is distinguishing. In this paper, we calculate the distinguishing threshold of a Cartesian product graph. Moreover, we calculate the number of non-equivalent distinguishing colorings of grids. |
| title | The number of distinguishing colorings of a Cartesian product graph |
| topic | Combinatorics 05C09, 05C15, 05C76 |
| url | https://arxiv.org/abs/2108.00635 |