一些奇异同谱图的性质研究
Research on the Property of Some Singularly Cospectral Graphs
摘要: 图G的能量E(G)是其邻接矩阵的所有特征值绝对值的和。如果两个图有相同的非零奇异值及重数，那么被称为奇异同谱图。奇异同谱图的刻画及性质研究对于图能量问题的推进有重要意义。本文利用克罗内克积和笛卡尔积运算，给出了一些新的关于奇异同谱图的性质。
Abstract: The energy E(G) of graph G is the sum of the absolute values of all the eigenvalues of its adjacency matrix. If two graphs have the same non-zero singular values with the same multiplicities, then they are called singularly cospectral. The study of the characterization and properties of singularly cospectral graphs is important for the advancement of the graph energy problem. In this paper, some new properties on singularly cospectral graphs are given using the Kronecker product and the Cartesian product.
文章引用：梁超凡, 姜艺淼. 一些奇异同谱图的性质研究[J]. 运筹与模糊学, 2023, 13(2): 1211-1217. https://doi.org/10.12677/ORF.2023.132124

参考文献

[1] Gutman, I. (1978) The Energy of a Graph. Graz Forschungszentrum Mathematisch Statistische Sektion Berichte, 103, 1-22.
[2] Nikiforov, V. (2016) Beyond Graph Energy: Norms of Graphs and Matrices. Linear Algebra and Its Applications, 506, 82-138. [Google Scholar] [CrossRef] 
[3] Abiad, A. and Alfaro, C.A. (2021) Enumeration of Cospectral and Coinvariant Graphs. Applied Mathematics and Computation, 408, Article ID: 126348. [Google Scholar] [CrossRef] 
[4] Godsil, C.D. and Mckay, B.D. (1982) Constructing Cospectral Graphs. Aequationes Mathematicae, 25, 257-268. [Google Scholar] [CrossRef] 
[5] Ji, Y., Gong, S. and Wang, W. (2020) Constructing Cospectral Bi-partite Graphs. Discrete Mathematics, 343, Article ID: 112020. [Google Scholar] [CrossRef] 
[6] Kannan, M.R., Pragada, S. and Wankhede, H. (2022) On the Construction of Cospectral Nonisomorphic Bipartite Graphs. Discrete Mathematics, 345, Article ID: 112916. [Google Scholar] [CrossRef] 
[7] Qiu, L., Ji, Y. and Wang, W. (2020) On a Theorem of Godsil and McKay Concerning the Construction of Cospectral Graphs. Linear Algebra and Its Applications, 603, 265-274. [Google Scholar] [CrossRef] 
[8] Conde, C., Dratman, E. and Grippo, L.N. (2022) Finding Sin-gularly Cospectral Graphs. Linear and Multilinear Algebra, 71, 496-512. [Google Scholar] [CrossRef] 
[9] Graham, A. (2018) Kronecker Products and Matrix Calculus with Applications. Courier Dover Publications, Chichester.
[10] Cvetković, D.M., Rowlinson, P. and Simić, S. (2010) An Introduction to the Theory of Graph Spectra. Cambridge University Press, Cambridge.

为你推荐