On some graphs associated with the finite alternating groups

被引：24

作者：

Bubboloni, D. ^{[1
]}

Iranmanesh, Mohammad A. ^{[2
]}

Shaker, S. M. ^{[2
]}

机构：

[1] Univ Firenze, Dipartimento Matemat & Informat U Dini, Florence, Italy

[2] Yazd Univ, Dept Math, Yazd 89195741, Iran

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 12期

关键词：

Alternating group; order graph; power graph; type graph; Primary: 05C25; Secondary: 20B30; POWER GRAPH;

D O I：

10.1080/00927872.2017.1307381

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P0(An), P0(An), P0(T(An)) and O0(An) be respectively the proper power graph, the proper quotient power graph, the proper power type graph and the proper order graph of the alternating group An, for n=3. We determine the number of the components of those graphs. In particular, we prove that the power graph P(An) is 2-connected if and only if the power type graph P(T(An)) is 2-connected, if and only if either n=3 or none of n,n-1,n-2,n2 and n-12 is a prime. We also give some information on the properties of those components.

引用

页码：5355 / 5373

页数：19

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