A note on solvable vertex stabilizers of s-transitive graphs of prime valency

Title:

A note on solvable vertex stabilizers of s-transitive graphs of prime valency

Creator:

Guo, Song-Tao, Hou, Hailong, and Xu, Yong

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:798d308d-0449-460a-87bd-e92c523605f5
uuid:798d308d-0449-460a-87bd-e92c523605f5
issn:0011-4642

Subject:

mathematics, symmetric graph, s-transitive graph, (G, s)-transitive graph, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

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 s\geq 5, and Gv the vertex stabilizer of a vertex v \in V (X). Suppose that Gv is solvable. Weiss (1974) proved that |Gv | p(p−1)^{2}. In this paper, we prove that Gv\cong (\mathbb{Z}_{p}\rtimes \mathbb{Z}_{m})× \mathbb{Z}_{n} for some positive integers m and n such that n | m and m | p − 1., Song-Tao Guo, Hailong Hou, Yong Xu., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

781-785

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:3

Harvested from:

CDK

Metadata only:

false