Finite 2-Geodesic Transitive Graphs of Prime Valency

被引：27

作者：

Devillers, Alice ^{[1
]}

Jin, Wei ^{[2
]}

Li, Cai Heng ^{[1
]}

Praeger, Cheryl E. ^{[1
]}

机构：

[1] Univ Western Australia, Sch Math & Stat, Ctr Math Symmetry & Computat, Crawley, WA 6009, Australia

[2] Jiangxi Univ Finance & Econ, Sch Stat, Res Ctr Appl Stat, Nanchang 330013, Jiangxi, Peoples R China

来源：

JOURNAL OF GRAPH THEORY | 2015年 / 80卷 / 01期

关键词：

2-geodesic transitive graph; 2-arc transitive graph; cover;

D O I：

10.1002/jgt.21835

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify noncomplete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of 2-geodesics. We prove that either is 2-arc transitive or the valency p satisfies p=1 (mod 4), and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph Kp+1 with automorphism group PSL(2,p)xZ2 and diameter 3.

引用

页码：18 / 27

页数：10

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