Smallest graphs with given automorphism group

被引：2

作者：

Deligeorgaki, Danai ^{[1
]}

机构：

[1] KTH Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2022年 / 56卷 / 02期

关键词：

Graph; Automorphism group; Minimum order; Generalised dicyclic group; Generalised quaternion group; VERTEX-MINIMAL GRAPHS;

D O I：

10.1007/s10801-022-01125-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a finite group G, denote by alpha(G) the minimum number of vertices of any graph Gamma having Aut(Gamma) congruent to G. In this paper, we prove that alpha(G) <= vertical bar G vertical bar, with specified exceptions. The exceptions include four infinite families of groups, and 17 other small groups. Additionally, we compute alpha(G) for the groups G such that alpha(G) > vertical bar G vertical bar where the value alpha(G) was previously unknown.

引用

页码：609 / 633

页数：25

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