Characterization of groups with planar, toroidal or projective planar (proper) reduced power graphs

被引：12

作者：

Anitha, T. ^{[1
]}

Rajkumar, R. ^{[1
]}

机构：

[1] Gandhigram Rural Inst Deemed Be Univ, Dept Math, Gandhigram 624302, Tamil Nadu, India

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 05期

关键词：

Group; reduced power graph; planar graph; toroidal graph; projective planar graph; KURATOWSKI THEOREM; GENUS;

D O I：

10.1142/S0219498820500991

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The reduced power graph RP(G) of a group G is the graph whose vertex set is the set of all elements of G, and two vertices u and v are adjacent in RP(G) if and only if < u > subset of < v > or < v > subset of < u >. The proper reduced power graph RP*(G) is the subgraph of RP(G) induced by the set of all nontrivial elements of G. In this paper, we study the planarity, toroidality and projective planarity of (proper) reduced power graph of a group.

引用

页数：16

共 46 条

[1] Power Graphs: A Survey [J].

Abawajy, Jemal ;

Kelarev, Andrei ;

Chowdhury, Morshed .

ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS, 2013, 1 (02) :125-147

[2] PLANAR, TOROIDAL, AND PROJECTIVE COMMUTING AND NONCOMMUTING GRAPHS [J].

Afkhami, M. ;

Farrokhi, M. D. G. ;

Khashyarmanesh, K. .

COMMUNICATIONS IN ALGEBRA, 2015, 43 (07) :2964-2970

[3] Some results on the power graphs of finite groups [J].

Alireza, Doostabadi ;

Ahmad, Erfanian ;

Abbas, Jafarzadeh .

SCIENCEASIA, 2015, 41 (01) :73-78

[4] On the power graph and the reduced power graph of a finite group [J].

Anitha, T. ;

Rajkumar, R. .

COMMUNICATIONS IN ALGEBRA, 2019, 47 (08) :3329-3339

[5]

Anitha T., 2018, PALEST J MATH, V7, P579

[6] A KURATOWSKI THEOREM FOR NONORIENTABLE SURFACES [J].

ARCHDEACON, D ;

HUNEKE, P .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1989, 46 (02) :173-231

[7] A KURATOWSKI THEOREM FOR THE PROJECTIVE PLANE [J].

ARCHDEACON, D .

JOURNAL OF GRAPH THEORY, 1981, 5 (03) :243-246

[8] Commuting involution graphs for symmetric groups [J].

Bates, C ;

Bundy, D ;

Perkins, S ;

Rowley, P .

JOURNAL OF ALGEBRA, 2003, 266 (01) :133-153

[9] SOLUTION TO KONIGS GRAPH EMBEDDING PROBLEM [J].

BODENDIEK, R ;

WAGNER, K .

MATHEMATISCHE NACHRICHTEN, 1989, 140 :251-272

[10] ON GROUPS OF EVEN ORDER [J].

BRAUER, R ;

FOWLER, KA .

ANNALS OF MATHEMATICS, 1955, 62 (03) :565-583

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