Geodesic
A note on solvable vertex stabilizers of $s$-transitive graphs of prime valency
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 781-785.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $m\mid p-1$.
DOI : 10.1007/s10587-015-0207-0
Classification : 05C25, 20B25
Keywords: symmetric graph; $s$-transitive graph; $(G, s)$-transitive graph 
@article{10_1007_s10587_015_0207_0,
     author = {Guo, Song-Tao and Hou, Hailong and Xu, Yong},
     title = {A note on solvable vertex stabilizers of $s$-transitive graphs of prime valency},
     journal = {Czechoslovak Mathematical Journal},
     pages = {781--785},
     publisher = {mathdoc},
     volume = {65},
     number = {3},
     year = {2015},
     doi = {10.1007/s10587-015-0207-0},
     mrnumber = {3407604},
     zbl = {06537691},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0207-0/}
}
TY  - JOUR
AU  - Guo, Song-Tao
AU  - Hou, Hailong
AU  - Xu, Yong
TI  - A note on solvable vertex stabilizers of $s$-transitive graphs of prime valency
JO  - Czechoslovak Mathematical Journal
PY  - 2015
SP  - 781
EP  - 785
VL  - 65
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0207-0/
DO  - 10.1007/s10587-015-0207-0
LA  - en
ID  - 10_1007_s10587_015_0207_0
ER  - 
%0 Journal Article
%A Guo, Song-Tao
%A Hou, Hailong
%A Xu, Yong
%T A note on solvable vertex stabilizers of $s$-transitive graphs of prime valency
%J Czechoslovak Mathematical Journal
%D 2015
%P 781-785
%V 65
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0207-0/
%R 10.1007/s10587-015-0207-0
%G en
%F 10_1007_s10587_015_0207_0
Guo, Song-Tao; Hou, Hailong; Xu, Yong. A note on solvable vertex stabilizers of $s$-transitive graphs of prime valency. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 781-785. doi : 10.1007/s10587-015-0207-0. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0207-0/

Cité par Sources :