On some graphs associated with the finite alternating groups

被引：22

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

共 50 条

[31] Domination Polynomial of the Commuting and Noncommuting Graphs of Some Finite Nonabelian Groups
Najmuddin, Nabilah
Sarmin, Nor Haniza
Erfanian, Ahmad
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH 2018): INNOVATIVE TECHNOLOGIES FOR MATHEMATICS & MATHEMATICS FOR TECHNOLOGICAL INNOVATION, 2019, 2184
[32] Permutability graphs of subgroups of some finite non-abelian groups
Rajkumar, R.
Devi, P.
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2016, 8 (03)
[33] Connectivity of superpower graphs of some non-abelian finite groups
Kumar, Ajay
Selvaganesh, Lavanya
Tamizh Chelvam, T.
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2023, 15 (04)
[34] On Some Graphs of Finite Metabelian Groups of Order Less Than 24
Gambo, Ibrahim
Sarmin, Nor Haniza
Omer, Sanaa Mohamed Saleh
MATEMATIKA, 2019, 35 (02) : 237 - 247
[35] Expansion properties of Cayley graphs of the alternating groups
Roichman, Y
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1997, 79 (02) : 281 - 297
[36] The diameter of proper power graphs of alternating groups
Pourghobadi, K.
Jafari, S. H.
UTILITAS MATHEMATICA, 2019, 113 : 121 - 129
[37] Metric properties of Cayley graphs of alternating groups
Olshevskyi, M. S.
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2021, 13 (02) : 545 - 581
[38] Superpower graphs of finite groups
Kumar, Ajay
Selvaganesh, Lavanya
Cameron, Peter J.
Tamizh Chelvam, T.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024,
[39] Factorization graphs of finite groups
Farrokhi, Mohammad D. G.
Azimi, Ali
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2021, 98 (1-2): : 183 - 199
[40] GRAPHS AND FINITE PERMUTATION GROUPS
SIMS, CC
MATHEMATISCHE ZEITSCHRIFT, 1967, 95 (01) : 76 - &

← 1 2 3 4 5 →