New structural results on tetravalent half-arc-transitive graphs

Rivera, Alejandra Ramos; Šparl, Primož

doi:10.1016/j.jctb.2018.08.006

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Cited by 10 publications

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References 29 publications

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“…It is well known that a finite half-arc-transitive is 2k-valent for some k ≥ 2. There are numerous constructions of half-arc-transitive graphs available, see for instance [1,2,11,12,14,17,18].…”

Section: Introductionmentioning

confidence: 99%

Half-arc-transitive graphs of arbitrarily large girth

Nedela,

Širáň‬

2023

Art Discrete Appl. Math.

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Section: Introductionmentioning

confidence: 99%

Half-arc-transitive graphs of arbitrarily large girth

Nedela,

Širáň‬

2023

Art Discrete Appl. Math.

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“…These results can often be used to improve our database of vertex-transitive graphs, see [10,11,27,28,29]. On the other hand, these databases can be used to test open problems or to formulate conjectures; see for example [9,31,37]. The spin off of this process is more theoretical work.…”

Section: Introductionmentioning

confidence: 99%

On the Number of Fixed Points of Automorphisms of Vertex-Transitive Graphs

Potočnik

Spiga

2021

Combinatorica

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Half-Arc-Transitive Graphs and the Fano Plane

Mačaj

Šparl

2021

Graphs and Combinatorics

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A subgroup G of the automorphism group of a graph Γ acts half-arc-transitively on Γ if the natural actions of G on the vertex-set and edge-set of Γ are both transitive, but the natural action of G on the arc-set of Γ is not transitive. When G = Aut(Γ) the graph Γ is said to be half-arc-transitive.Given a bipartite cubic graph with a certain degree of symmetry two covering constructions that provide innitely many tetravalent graphs admitting half-arc-transitive groups of automorphisms are introduced. Symmetry properties of constructed graphs are investigated. In the second part of the paper the two constructions are applied to the Heawood graph, the well-known incidence graph of the Fano plane. It is proved that the members of the innite family resulting from one of the two constructions are all half-arc-transitive, and that the innite family resulting from the second construction contains a mysterious family of arc-transitive graphs that emerged within the classication of tightly attached half-arc-transitive graphs of valence 4 back in 1998 and 2008.

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New structural results on tetravalent half-arc-transitive graphs

Cited by 10 publications

References 29 publications

Half-arc-transitive graphs of arbitrarily large girth

Half-arc-transitive graphs of arbitrarily large girth

On the Number of Fixed Points of Automorphisms of Vertex-Transitive Graphs

Half-Arc-Transitive Graphs and the Fano Plane

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