On the independence number of the power graph of a finite group

被引：14

作者：

Ma, Xuanlong ^{[1
]}

Fu, Ruiqin ^{[1
]}

Lu, Xuefei ^{[1
]}

机构：

[1] Xian Shiyou Univ, Sch Sci, Xian 710065, Shaanxi, Peoples R China

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2018年 / 29卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Power graph; Finite group; Independence number; SEMIGROUPS;

D O I：

10.1016/j.indag.2018.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The power graph Gamma(G) of a finite group G is the graph whose vertex set is G, two distinct elements being adjacent if one is a power of the other. In this paper, we give sharp lower and upper bounds for the independence number of Gamma(G) and characterize the groups achieving the bounds. Moreover, we determine the independence number of Gamma(G) if G is cyclic, dihedral or generalized quaternion. Finally, we classify all finite groups G whose power graphs have independence number 3 or n 2, where n is the order of G. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：794 / 806

页数：13

共 50 条

[21] Certain properties of the power graph associated with a finite group [J].

Moghaddamfar, A. R. ;

Rahbariyan, S. ;

Shi, W. J. .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (07)

[22] Notes on the diameter of the complement of the power graph of a finite group [J].

Ma, Xuanlong ;

Doostabadi, Alireza ;

Wang, Kaishun .

ARS MATHEMATICA CONTEMPORANEA, 2025, 25 (01)

[23] On the structure of the power graph and the enhanced power graph of a group [J].

Aalipour, Ghodratollah ;

Akbari, Saieed ;

Cameron, Peter J. ;

Nikandish, Reza ;

Shaveisi, Farzad .

ELECTRONIC JOURNAL OF COMBINATORICS, 2017, 24 (03)

[24] The power graph of a finite group, II [J].

Cameron, Peter J. .

JOURNAL OF GROUP THEORY, 2010, 13 (06) :779-783

[25] The Undirected Power Graph of a Finite Group [J].

G. R. Pourgholi ;

H. Yousefi-Azari ;

A. R. Ashrafi .

Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38 :1517-1525

[26] On the enhanced power graph of a finite group [J].

Panda, Ramesh Prasad ;

Dalal, Sandeep ;

Kumar, Jitender .

COMMUNICATIONS IN ALGEBRA, 2021, 49 (04) :1697-1716

[27] The Undirected Power Graph of a Finite Group [J].

Pourgholi, G. R. ;

Yousefi-Azari, H. ;

Ashrafi, A. R. .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2015, 38 (04) :1517-1525

[28] A NOTE ON THE POWER GRAPH OF A FINITE GROUP [J].

Mehranian, Zeinab ;

Gholami, Ahmad ;

Ashrafi, Ali Reza .

INTERNATIONAL JOURNAL OF GROUP THEORY, 2016, 5 (01) :1-10

[29] The number of edges in power graph of finite groups [J].

Jafari, S. H. .

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (03)

[30] The power graph on the conjugacy classes of a finite group [J].

S. M. Robati .

Acta Mathematica Hungarica, 2016, 148 :109-116

← 1 2 3 4 5 →