Classification of groups according to the number of end vertices in the coprime graph

被引：1

作者：

Alraqad, Tariq A. ^{[1
]}

Saeed, Muhammad S. ^{[1
]}

Alshawarbeh, Etaf S. ^{[1
]}

机构：

[1] Univ Hail, Dept Math, Hail, Saudi Arabia

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2021年 / 52卷 / 01期

关键词：

Coprime Graphs; Finite Groups; End Vertices;

D O I：

10.1007/s13226-021-00132-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we characterize groups according to the number of end vertices in the associated coprime graphs. An upper bound on the order of the group that depends on the number of end vertices is obtained. We also prove that 2-groups are the only groups whose coprime graphs have odd number of end vertices. Classifications of groups with small number of end vertices in the coprime graphs are given. We give a complete answer to [4, Question 3.7], where we show that Z(4) and Z(2) X Z(2) are the only groups whose coprime graph has exactly three end vertices.

引用

页码：105 / 111

页数：7

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