Hexavalent (G, s)-transitive graphs

被引：11

作者：

Guo, Song-Tao ^{[1
]}

Hua, Xiao-Hui ^{[2
]}

Li, Yan-Tao ^{[3
]}

机构：

[1] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China

[2] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China

[3] Beijing Union Univ, Coll Arts & Sci, Beijing 100091, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2013年 / 63卷 / 04期

基金：

中国国家自然科学基金;

关键词：

symmetric graph; s-transitive graph; (G; s)-transitive graph; S-TRANSITIVE GRAPHS; ARC TRANSITIVITY;

D O I：

10.1007/s10587-013-0062-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a finite simple undirected graph with a subgroup G of the full automorphism group Aut(X). Then X is said to be (G, s)-transitive for a positive integer s, if G is transitive on s-arcs but not on (s + 1)-arcs, and s-transitive if it is (Aut(X), s)-transitive. Let G (v) be a stabilizer of a vertex v a V (X) in G. Up to now, the structures of vertex stabilizers G (v) of cubic, tetravalent or pentavalent (G, s)-transitive graphs are known. Thus, in this paper, we give the structure of the vertex stabilizers G (v) of connected hexavalent (G, s)-transitive graphs.

引用

页码：923 / 931

页数：9

共 21 条

[1] The Magma algebra system .1. The user language [J].

Bosma, W ;

Cannon, J ;

Playoust, C .

JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265

[2]

Conway J. H., 1985, ATLAS of Finite Groups

[3]

Dixon J.D., 1996, GRADUATE TEXTS MATH, V163, DOI DOI 10.1007/978-1-4612-0731-3

[4] REGULAR GROUPS OF AUTOMORPHISMS OF CUBIC GRAPHS [J].

DJOKOVIC, DZ ;

MILLER, GL .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1980, 29 (02) :195-230

[5] ARC TRANSITIVITY IN GRAPHS-3 [J].

GARDINER, A .

QUARTERLY JOURNAL OF MATHEMATICS, 1976, 27 (107) :313-323

[6] ARC TRANSITIVITY IN GRAPHS .2. [J].

GARDINER, A .

QUARTERLY JOURNAL OF MATHEMATICS, 1974, 25 (98) :163-167

[7] ARC TRANSITIVITY IN GRAPHS [J].

GARDINER, A .

QUARTERLY JOURNAL OF MATHEMATICS, 1973, 24 (95) :399-407

[8] A note on pentavalent s-transitive graphs [J].

Guo, Song-Tao ;

Feng, Yan-Quan .

DISCRETE MATHEMATICS, 2012, 312 (15) :2214-2216

[9] The finite vertex-primitive and vertex-biprimitive s-transitive graphs for s ≥ 4 [J].

Li, CH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (09) :3511-3529

[10] TETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED VERTEX-STABILIZERS [J].

Potocnik, Primoz ;

Spiga, Pablo ;

Verret, Gabriel .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2011, 84 (01) :79-89

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