Stability of Rose Window graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913460813561856 |
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| author | Ahanjideh, Milad Kovács, István Kutnar, Klavdija |
| author_facet | Ahanjideh, Milad Kovács, István Kutnar, Klavdija |
| contents | A graph $Γ$ is said to be stable if for the direct product $Γ\times\mathbf{K}_2$, ${\rm Aut}(Γ\times \mathbf{K}_2)$ is isomorphic to ${\rm Aut}(Γ) \times \mathbb{Z}_2$; otherwise, it is called unstable. An unstable graph is called non-trivially unstable when it is not bipartite and no two vertices have the same neighborhood. Wilson described nine families of unstable Rose Window graphs and conjectured that these contain all non-trivially unstable Rose Window graphs (2008). In this paper we show that the conjecture is true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01619 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of Rose Window graphs Ahanjideh, Milad Kovács, István Kutnar, Klavdija Combinatorics A graph $Γ$ is said to be stable if for the direct product $Γ\times\mathbf{K}_2$, ${\rm Aut}(Γ\times \mathbf{K}_2)$ is isomorphic to ${\rm Aut}(Γ) \times \mathbb{Z}_2$; otherwise, it is called unstable. An unstable graph is called non-trivially unstable when it is not bipartite and no two vertices have the same neighborhood. Wilson described nine families of unstable Rose Window graphs and conjectured that these contain all non-trivially unstable Rose Window graphs (2008). In this paper we show that the conjecture is true. |
| title | Stability of Rose Window graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2306.01619 |