| Title:
|
A note on solvable vertex stabilizers of $s$-transitive graphs of prime valency (English) |
| Author:
|
Guo, Song-Tao |
| Author:
|
Hou, Hailong |
| Author:
|
Xu, Yong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
781-785 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A graph $X$, with a group $G$ of automorphisms of $X$, is said to be $(G,s)$-transitive, for some $s\geq 1$, if $G$ is transitive on $s$-arcs but not on $(s+1)$-arcs. Let $X$ be a connected $(G,s)$-transitive graph of prime valency $p\geq 5$, and $G_v$ the vertex stabilizer of a vertex $v\in V(X)$. Suppose that $G_v$ is solvable. Weiss (1974) proved that $|G_v|\mid p(p-1)^2$. In this paper, we prove that $G_v\cong (\mathbb Z_p\rtimes \mathbb Z_m)\times \mathbb Z_n$ for some positive integers $m$ and $n$ such that $n\div m$ and $m\mid p-1$. (English) |
| Keyword:
|
symmetric graph |
| Keyword:
|
$s$-transitive graph |
| Keyword:
|
$(G,s)$-transitive graph |
| MSC:
|
05C25 |
| MSC:
|
20B25 |
| idZBL:
|
Zbl 06537691 |
| idMR:
|
MR3407604 |
| DOI:
|
10.1007/s10587-015-0207-0 |
| . |
| Date available:
|
2015-10-04T18:17:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144442 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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