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

2019/12/23 by Pablo Spiga, Spiga, Pablo, Binzhou Xia +1 · 2 citations
Mathematics · Computer Science · #Finite Group Theory Research #Coding theory and cryptography #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1912.10695

Abstract

We prove that, given a finite graph Σ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of Σ. 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 2⁸ 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.

Cited by

• On automorphism groups of half-arc-transitive tetravalent graphs
• On tetravalent half-arc-transitive graphs

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