Arc-transitive graphs of valency 8 have a semiregular automorphism
Gabriel Verret
TL;DR
This paper proves that all arc-transitive graphs with valency 8 possess a semiregular automorphism, confirming a special case of the polycirculant conjecture.
Contribution
It provides the first proof of the conjecture for the smallest open case of valency 8 in arc-transitive graphs.
Findings
Confirmed the polycirculant conjecture for valency 8 arc-transitive graphs
Established existence of semiregular automorphisms in this class
Solved the smallest open case of the conjecture
Abstract
One version of the polycirculant conjecture states that every vertex-transitive graph has a semiregular automorphism. We give a proof of the conjecture in the arc-transitive case for graphs of valency 8, which was the smallest open case.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Graph Theory Research · Limits and Structures in Graph Theory