Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909075646709760 |
|---|---|
| author | Poznanovic, Nemanja Praeger, Cheryl E. |
| author_facet | Poznanovic, Nemanja Praeger, Cheryl E. |
| contents | Let $\mathcal{OG}(4)$ denote the family of all graph-group pairs $(Γ, G)$ where $Γ$ is finite, 4-valent, connected, and $G$-oriented ($G$-half-arc-transitive). A subfamily of $\mathcal{OG}(4)$ has recently been identified as `basic' in the sense that all graphs in this family are normal covers of at least one basic member. In this paper we provide a description of such basic pairs which have at least one $G$-normal quotient which is isomorphic to a cycle graph. In doing so, we produce many new infinite families of examples and solve several problems posed in the recent literature on this topic. This result completes a research project aiming to provide a description of all basic pairs in $\mathcal{OG}(4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients Poznanovic, Nemanja Praeger, Cheryl E. Combinatorics Let $\mathcal{OG}(4)$ denote the family of all graph-group pairs $(Γ, G)$ where $Γ$ is finite, 4-valent, connected, and $G$-oriented ($G$-half-arc-transitive). A subfamily of $\mathcal{OG}(4)$ has recently been identified as `basic' in the sense that all graphs in this family are normal covers of at least one basic member. In this paper we provide a description of such basic pairs which have at least one $G$-normal quotient which is isomorphic to a cycle graph. In doing so, we produce many new infinite families of examples and solve several problems posed in the recent literature on this topic. This result completes a research project aiming to provide a description of all basic pairs in $\mathcal{OG}(4)$. |
| title | Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.08907 |