Normal covers of 2-arc-transitive graphs of prime-power order

Conder, Marston D. E. (author), Potočnik, Primož (author)

In a paper by Cai Heng Li in Bull. London Math. Soc. 33 (2001), it was suggested that ‘non-basic’ $2$-arc-transitive graphs of prime-power order that occur as normal covers of smaller $2$-arc-transitive graphs might be rare and difficult to construct. This note describes some of the background to Li’s suggestion, and gives some examples of small valency, and then goes on to show that in fact there are infinitely many examples of valency $d$, for every integer $d \ge 2$. It is also noted that the hypercubes $(Q_n)$ for $n \ge 4$ even, together with a $2$-arc-transitive group $G$ of index $2$ in ${\rm Aut}(Q_n)$, show that the claims of Corollary 1.2 in the above paper by Li are not quite correct.

• Language: English
• Keywords: graphs, s-arc-transitive, normal cover
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2025
• Year: 2025
• Number of pages: Str. 469-478
• Numbering: Vol. 8, iss. 2
• PID: 20.500.12556/RUL-170481
• UDC: 519.17
• ISSN on article: 2589-5486
• DOI: 10.5802/alco.415
• COBISS.SI-ID: 241575683
• Publication date in RUL: 07.07.2025

Record is a part of a journal

• Title: Algebraic combinatorics
• Publisher: MathOA
• ISSN: 2589-5486
• COBISS.SI-ID: 1540134596

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