Basic Tetravalent Oriented Graphs of Independent-Cycle Type
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917723159658496 |
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| author | Poznanovic, Nemanja Praeger, Cheryl E. |
| author_facet | Poznanovic, Nemanja Praeger, Cheryl E. |
| contents | The family $\mathcal{OG}(4)$ consisting of graph-group pairs $(Γ, G)$, where $Γ$ is a finite, connected, 4-valent graph admitting a $G$-vertex-, and $G$-edge-transitive, but not $G$-arc-transitive action, has recently been examined using a normal quotient methodology. A subfamily of $\mathcal{OG}(4)$ has been identified as `basic', due to the fact that all members of $\mathcal{OG}(4)$ are normal covers of at least one basic pair. We provide an explicit classification of those basic pairs $(Γ, G)$ which have at least two independent cyclic $G$-normal quotients (these are $G$-normal quotients which are not extendable to a common cyclic normal quotient). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Basic Tetravalent Oriented Graphs of Independent-Cycle Type Poznanovic, Nemanja Praeger, Cheryl E. Combinatorics Group Theory 05C25 The family $\mathcal{OG}(4)$ consisting of graph-group pairs $(Γ, G)$, where $Γ$ is a finite, connected, 4-valent graph admitting a $G$-vertex-, and $G$-edge-transitive, but not $G$-arc-transitive action, has recently been examined using a normal quotient methodology. A subfamily of $\mathcal{OG}(4)$ has been identified as `basic', due to the fact that all members of $\mathcal{OG}(4)$ are normal covers of at least one basic pair. We provide an explicit classification of those basic pairs $(Γ, G)$ which have at least two independent cyclic $G$-normal quotients (these are $G$-normal quotients which are not extendable to a common cyclic normal quotient). |
| title | Basic Tetravalent Oriented Graphs of Independent-Cycle Type |
| topic | Combinatorics Group Theory 05C25 |
| url | https://arxiv.org/abs/2407.11411 |