Four Constructions of Highly Symmetric Tetravalent Graphs

被引：4

作者：

Hill, Aaron ^{[1
]}

Wilson, Steve ^{[2
]}

机构：

[1] Univ N Texas, Dept Math, Denton, TX 76203 USA

[2] No Arizona Univ, Dept Math & Stat, Flagstaff, AZ 86011 USA

来源：

JOURNAL OF GRAPH THEORY | 2012年 / 71卷 / 03期

基金：

美国国家科学基金会;

关键词：

Graph; Map; Symmetry; Capping; Dart; Cubic Graph; Corners; TRANSITIVE GROUP-ACTIONS; FINITE GRAPHS; REGULAR MAPS; VALENCY-4;

D O I：

10.1002/jgt.20520

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a connected, dart-transitive, cubic graph, constructions of its Hexagonal Capping and its Dart Graph are considered. In each case, the result is a tetravalent graph which inherits symmetry from the original graph and is a covering of the line graph.Similar constructions are then applied to a map (a cellular embedding of a graph in a surface) giving tetravalent coverings of the medial graph. For each construction, conditions on the graph or the map to make the constructed graph dart-transitive, semisymmetric or 12-transitive are considered.

引用

页码：229 / 244

页数：16

共 19 条

[1] A census of semisymmetric cubic graphs on up to 768 vertices [J].