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arXiv · 2401.08907

Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients

Nemanja Poznanovic·Cheryl E. Praeger
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Abstract

Let $\mathcal{OG}(4)$ denote the family of all graph-group pairs $(\Gamma, G)$ where $\Gamma$ 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 $\mathcal{OG}(4)$.

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BibTeXRIS

Nemanja Poznanovic, Cheryl E. Praeger. 2024-01-17. Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients. https://arxiv.org/abs/2401.08907

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