Constructing infinitely many half-arc-transitive covers of tetravalent graphs

DOI10.1016/J.JCTA.2021.105406arXiv1912.10695MaRDI QIDQ6331657

Pablo Spiga, Binzhou Xia

Publication date: 23 December 2019

Abstract: We prove that, given a finite graph $Sigma$ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of $Sigma$. Applying this result, we establish the existence of infinite families of finite tetravalent half-arc-transitive graphs with certain vertex stabilizers, and classify the vertex stabilizers up to order $2^8$ of finite connected tetravalent half-arc-transitive graphs. This sheds some new light on the longstanding problem of classifying the vertex stabilizers of finite tetravalent half-arc-transitive graphs.

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Group actions on combinatorial structures (05E18)

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