| Title: | Normal covers of 2-arc-transitive graphs of prime-power order |
|---|
| Authors: | ID Conder, Marston D. E. (Author)
ID Potočnik, Primož (Author) |
|---|
| Files: |  PDF - Presentation file, download (918,24 KB)
MD5: 50DEC5E09001925DA72B83A09E70AEE9
 URL - Source URL, visit https://alco.centre-mersenne.org/articles/10.5802/alco.415/
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | graphs, s-arc-transitive, normal cover |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.01.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 469-478 |
|---|
| Numbering: | Vol. 8, iss. 2 |
|---|
| PID: | 20.500.12556/DiRROS-22864  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 2589-5486 |
|---|
| DOI: | 10.5802/alco.415 |
|---|
| COBISS.SI-ID: | 241575683 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 07.07.2025 |
|---|
| Views: | 319 |
|---|
| Downloads: | 194 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
