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.

Spiga, P., Xia, B. (2021). Constructing infinitely many half-arc-transitive covers of tetravalent graphs. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 180 [10.1016/j.jcta.2021.105406].

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

Spiga P.
;
2021

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.
Articolo in rivista - Articolo scientifico
Concentric group; Half-arc-transitive; Normal cover; Normal quotient; Vertex stabilizer;
English
2021
180
105406
open
Spiga, P., Xia, B. (2021). Constructing infinitely many half-arc-transitive covers of tetravalent graphs. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 180 [10.1016/j.jcta.2021.105406].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/416064
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