星图的Seidel谱和完全图的加权Estrada指数
Seidel Spectrum of Star Graphs and the Weighted Estrada Index of Complete Graphs
DOI: 10.12677/aam.2025.1411476, PDF,   
作者: 扈嘉萱, 儒孜·买司地克*：新疆师范大学数学与科学学院，新疆 乌鲁木齐
关键词: 加权邻接矩阵；Estrada指数；Seidel矩阵；Weighted Adjacency Matrix； Estrada Index； Seidel Matrix
摘要: 本文通过加权邻接矩阵求解出完全图的加权Estrada指数，并给出了完全二部图删去一个匹配后所得图的加权Estrada指数。同时结合Sherman-Morrison公式与矩阵行列式引理得到了星图的Seidel谱，还分别计算出了完全二部图和双团图所对应的距离拉普拉斯特征值与距离无符号拉普拉斯特征值。
Abstract: This paper computes the weighted Estrada index of complete graphs using the weighted adjacency matrix and provides the weighted Estrada index of graphs obtained by removing a matching from complete bipartite graphs. Additionally, by combining the Sherman-Morrison formula and the matrix determinant lemma, the Seidel spectrum of star graphs is derived. The distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of complete bipartite graphs and double clique graphs are also calculated, respectively.
文章引用：扈嘉萱, 儒孜·买司地克. 星图的Seidel谱和完全图的加权Estrada指数[J]. 应用数学进展, 2025, 14(11): 199-208. https://doi.org/10.12677/aam.2025.1411476

参考文献

[1] Estrada, E. (2000) Characterization of 3D Molecular Structure. Chemical Physics Letters, 319, 713-718. [Google Scholar] [CrossRef] 
[2] 范益政, 郑剑. 一类非线性超图的Estrada指数[J]. 安徽大学学报(自然科学版), 2024, 48(6): 1-8.
[3] 徐薇薇. 图的Estrada指数[D]: [硕士学位论文]. 上海: 上海大学, 2013.
[4] Xu, B., Li, S., Yu, R. and Zhao, Q. (2019) On the Spectral Radius and Energy of the Weighted Adjacency Matrix of a Graph. Applied Mathematics and Computation, 340, 156-163. [Google Scholar] [CrossRef] 
[5] Aouchiche, M. and Hansen, P. (2013) Two Laplacians for the Distance Matrix of a Graph. Linear Algebra and Its Applications, 439, 21-33. [Google Scholar] [CrossRef] 
[6] 卢鹏丽, 刘文智. Indu-Bala乘积图的广义距离谱[J]. 哈尔滨工程大学学报, 2020, 41(9): 1366-1370.
[7] Sherman, J. and Morrison, W.J. (1950) Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix. Annals of Mathematical Statistics, 21, 124-127. [Google Scholar] [CrossRef] 
[8] Duncan, W.J. (1947) The Algebra of Continuum Systems. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 459-467.
[9] Zhang, F. (2006) The Schur Complement and Its Applications. Springer Science Business Media. [Google Scholar] [CrossRef] 

为你推荐