Properties of Commuting Graphs over Semidihedral Groups

被引：6

作者：

Cheng, Tao ^{[1
]}

Dehmer, Matthias ^{[2
,3
,4
,5
]}

Emmert-Streib, Frank ^{[6
,7
]}

Li, Yongtao ^{[8
]}

Liu, Weijun ^{[9
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250358, Peoples R China

[2] Swiss Distance Univ Appl Sci, Dept Comp Sci, CH-3900 Brig, Switzerland

[3] Nankai Univ, Coll Artificial Intelligence, Tianjin 300350, Peoples R China

[4] Xian Technol Univ, Sch Sci, Xian 710021, Peoples R China

[5] UMIT, Dept Biomed Comp Sci & Mechatron, A-6060 Hall In Tirol, Austria

[6] Tampere Univ, Dept Signal Proc, Predict Med & Data Analyt Lab, Tampere 33100, Finland

[7] Inst Biosci & Med Technol, Tampere 33520, Finland

[8] Hunan Univ, Sch Math, Changsha 410082, Peoples R China

[9] Cent South Univ, Sch Math & Stat, New Campus, Changsha 410083, Peoples R China

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 01期

关键词：

graph spectrum; semidihedral groups; commuting graph; spectral radius;

D O I：

10.3390/sym13010103

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper considers commuting graphs over the semidihedral group SD8n. We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n >= 15 or even n >= 2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n. We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

引用

页码：1 / 15

页数：15

共 13 条

[1] The connectivity and the spectral radius of commuting graphs on certain finite groups
Ali, Fawad
Li, Yongjin
[J]. LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (16) : 2945 - 2958
[2] Brouwer AE, 2012, UNIVERSITEXT, P1, DOI 10.1007/978-1-4614-1939-6
[3] The connectivity of commuting graphs
Bundy, D.
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2006, 113 (06) : 995 - 1007
[4] Directed Strongly Regular Cayley Graphs over Metacyclic Groups of Order 4n
Cheng, Tao
Feng, Lihua
Liu, Weijun
[J]. MATHEMATICS, 2019, 7 (11)
[5] Integral Cayley graphs over dicyclic group
Cheng, Tao
Feng, Lihua
Huang, Hualin
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 566 : 121 - 137
[6] Cvetkovic D., 2010, London Mathematical Society Student Texts, V75
[7] Gutman I., 1978, Ber. Math. Statist. Sekt. Forsch-ungszentram Graz, V103, P1, DOI DOI 10.1088/1742-5468/2008/10/P10008
[8] Harary F., 1969, Graph theory
[9] Li X., 2012, Graph Energy
[10] Mohar B., 1991, Graph Theory Combinatorics and Applications, V2, P871

← 1 2 →