Locally Symmetric Graphs of Girth 4

被引：2

作者：

Perles, Micha A. ^{[1
]}

Martini, Horst ^{[2
]}

Kupitz, Yaakov S. ^{[1
]}

机构：

[1] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel

[2] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

来源：

JOURNAL OF GRAPH THEORY | 2013年 / 73卷 / 01期

关键词：

automorphism group; bipartite graph; Heawood and co-Heawood graph; Coxeter graph; Fano plane; girth of a graph; (hyperbolic) honeycomb; Klein map {7; 3}8; k-regular graph; locally symmetric graph; matching; 120-cell; Petersen graph; regular dodecahedron; Riemann surface; tessellation; bathroom tiling; MSC (2000):05C12; 05C30; 51E30; 94C15;

D O I：

10.1002/jgt.21657

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify the family of connected, locally symmetric graphs of girth 4 (finite and infinite). They are all regular, with the exception of the complete bipartite graph Km,n(2m<n). There are, up to isomorphism, exactly four such k-regular graphs for every 4k<, one for k=2, two for k=3, and exactly three for every infinite cardinal k. In the last paragraph, we consider locally symmetric graphs of girth >4.

引用

页码：44 / 65

页数：22

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