|
|
Pure Mathematics 2024
一类p-群的非交换图的谱性质
|
Abstract:
有限非交换群的非交换图是一类简单无向图，它以群的非中心元为顶点，两顶点相邻接当且仅当它们的乘积不可交换。本文研究了p3阶群的非交换图的相关谱性质，包括邻接谱、拉普拉斯谱，拟拉普拉斯谱以及正规拉普拉斯谱等。
Non-commuting graphs of finite non-abelian groups are a class of simple undirected graphs that take the non-central elements of the group as vertices, and two vertices are adjacent if and only if their product is non commutative. This paper investigates the spectral properties of non-commuting graphs of groups of order p3, including adjacency spectra, Laplace spectra, quasi-Laplace spectra, and normal-Laplace spectra.
| [1] | Lennox, J.C. and Wiegold, J. (1981) Extensions of a Problem of Paul Erd？s on Groups. Journal of the Australian Mathematical Society, 31, 459-463. https://doi.org/10.1017/S1446788700024253 |
| [2] | Longobardi, P. (2001) On Locally Graded Groups with an Engel Condition on Infinite Subsets. Archiv der Mathematik, 76, 88-90. https://doi.org/10.1007/s000130050546 |
| [3] | Mahmoud, R., et al. (2017) On the Energy of Non-Commuting Graph of Dihedral Groups. AIP Conference Proceedings, 1830, Article 070011. https://doi.org/10.1063/1.4980960 |
| [4] | Wu, B.-F., Lou, Y.-Y. and He, C.-X. (2014) Signless Laplacian and Normalized and Normalized Laplacian on the H-Join Operation of Graphs. Discrete Mathematics, Algorithms and Ap-plications, 6, Article ID: 1450046.
https://doi.org/10.1142/S1793830914500463 |
| [5] | Torktaz, M. and Ashrafi, A.R. (2019) Spectral Properties of the Commuting Graphs of Certain Groups. AKCE International Journal of Graphs and Combinatorics, 16, 300-309. https://doi.org/10.1016/j.akcej.2018.09.006 |
| [6] | Grone, R., Merris, R. and Sunder, V.S. (1990) The Laplacian Spectrum of a Graph. SIAM Journal on Matrix Analysis and Applications, 11, 218-238. https://doi.org/10.1137/0611016 |
| [7] | Dutta, P., Dutta, J. and Nath, R.K. (2018) Laplacian Spectrum of Non-Commuting Graphs of Finite Groups. Indian Journal of Pure and Applied Mathematics, 49, 205-216. https://doi.org/10.1007/s13226-018-0263-x |
| [8] | Douglas B. West. 图论导引[M]. 骆吉洲, 李建中, 译. 北京: 机械工业出版社, 2020. |
| [9] | Abdollahi, A., Akbari, S. and Maimani, H.R. (2006) Non-Commuting Graph of a Group. Journal of Algebra, 298, 468-492. https://doi.org/10.1016/j.jalgebra.2006.02.015 |
| [10] | Brouwer, A.E. and Haemers, W.H. (2012) Spectra of Graphs. Springer, New York.
https://doi.org/10.1007/978-1-4614-1939-6 |
| [11] | 徐明曜. 有限群初步(现代数学基础丛书152) [M]. 北京: 科学出版社, 2014. |
| [12] | Biggs, N. (1994) Algebraic Graph Theory. 2nd Edition, Cambridge University Press, Cam-bridge. |
| [13] | Cvetkovi？, D.M., Doob, M. and Sachs, H. (1980) Spectra of Graphs: Theory and Application. Academic Press, Cambridge. |
