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

被引：12

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

[41] On the Metric Dimension of the Reduced Power Graph of a Finite Group [J].

Ma, Xuanlong ;

Li, Lan .

TAIWANESE JOURNAL OF MATHEMATICS, 2022, 26 (01) :1-15

[42] The structure and metric dimension of the power graph of a finite group [J].

Feng, Min ;

Ma, Xuanlong ;

Wang, Kaishun .

EUROPEAN JOURNAL OF COMBINATORICS, 2015, 43 :82-97

[43] Vertex connectivity of the power graph of a finite cyclic group [J].

Chattopadhyay, Sriparna ;

Patra, Kamal Lochan ;

Sahoo, Binod Kumar .

DISCRETE APPLIED MATHEMATICS, 2019, 266 :259-271

[44] On the minimum degree of the power graph of a finite cyclic group [J].

Panda, Ramesh Prasad ;

Patra, Kamal Lochan ;

Sahoo, Binod Kumar .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (03)

[45] A lower bound on the independence number of a graph [J].

Harant, J .

DISCRETE MATHEMATICS, 1998, 188 (1-3) :239-243

[46] On the clique number and independence number of the cyclic graph of a semigroup [J].

Dalal, Sandeep ;

Kumar, Jitender ;

Singh, Siddharth .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024, 23 (05)

[47] On the Connectivity and Independence Number of Power Graphs of Groups [J].

Peter J. Cameron ;

Sayyed Heidar Jafari .

Graphs and Combinatorics, 2020, 36 :895-904

[48] On the Connectivity and Independence Number of Power Graphs of Groups [J].

Cameron, Peter J. ;

Jafari, Sayyed Heidar .

GRAPHS AND COMBINATORICS, 2020, 36 (03) :895-904

[49] THE ORDER DIVISOR GRAPH OF A FINITE GROUP [J].

Liu, Xiu ;

Ma, Xuanlong .

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2020, 73 (03) :339-347

[50] Vertex connectivity of the power graph of a finite cyclic group II [J].

Chattopadhyay, Sriparna ;

Patra, Kamal Lochan ;

Sahoo, Binod Kumar .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (02)

← 1 2 3 4 5 →