几类图的推广的拉普拉斯矩阵的特征多项式
The Characteristic Polynomial of Generalized Laplace Matrix of Several Kinds of Graphs
DOI: 10.12677/AAM.2017.66092, PDF, HTML, XML, 下载: 1,679  浏览: 2,267  国家自然科学基金支持
作者: 梁静, 赵海兴, 张科：青海师范大学计算机学院，青海 西宁；刘远超：青海师范大学数学与统计学院，青海 西宁
关键词: 拉普拉斯矩阵；推广的拉普拉斯矩阵；特征多项式；特征根；Laplace Matrix； Generalized Laplace Matrix； Characteristic Polynomial； Eigenvalue
摘要: 本文主要研究几类图的推广的拉普拉斯矩阵的特征多项式。用A(G)表示有n个顶点的简单图G的邻接矩阵，D(G)表示图G的顶点度对角矩阵。图G的拉普拉斯矩阵为，推广的拉普拉斯矩阵设为 。根据完全图和二部图的推广的拉普拉斯矩阵的特征多项式的结果，可以知道推广式中k分别取−1、0、1时，即是无符号拉普拉斯矩阵、邻接矩阵、拉普拉斯矩阵的相应的结果。
Abstract: In this paper, we mainly study the characteristic polynomial of the generalized Laplace matrix of several kinds of graphs. The adjacency matrix of a simple graph with n vertexes represented by A(G), D(G) represents the vertex degree diagonal matrix of graph G. The Laplace matrix of G is , the generalized Laplace matrix is set to . We can know the promotion of the k are taken −1, 0, 1. That is, the corresponding results of the unsigned Laplace matrix, adjacency matrix and the Laplace matrix.
文章引用：梁静, 赵海兴, 张科, 刘远超. 几类图的推广的拉普拉斯矩阵的特征多项式[J]. 应用数学进展, 2017, 6(6): 763-767. https://doi.org/10.12677/AAM.2017.66092

参考文献

[1] Bondy, J.A. and Murty, U.S.R. (1976) Graph Theory with Application. The Macmilian Press Ltd., 115-120.
https://doi.org/10.1007/978-1-349-03521-2
[2] Brouwer, A.E. and Haemers, W.H. (2011) Spectra of Graphs. Springer, 81-82.
[3] Cvetkovicid, Doob, M. and Scachs, H. (1980) Spectra of Graphs—Theory and Application. Academic Press, New York.
[4] Brualdi, R.A. and Hoffman, A.J. (1985) On the Spectral Radius of (0,1)-Mantrices. Linear Algebra and Its Applications, 69, 133-146.
https://doi.org/10.1016/0024-3795(85)90092-8
[5] Cvetkovic, D., Rowlinson, P. and Simio, S. (2007) Singless Lap-lacian of Finite Graphs. Linear Algebra and Its Applications, 423, 155-171.
[6] Mohar, B. The Laplacian Spectrum of Graphs. Department of Mathematics, University of Ljubljana, Ljubljana.
[7] 赵国鹏. 完全多部图的拉普拉斯特征多项式[J]. 纺织高校基础科学学报, 2011, 24(2): 243-245.
[8] 卢世芳, 卫良, 赵海兴. 完全3-部图的无符号Laplace谱[J]. 山东大学学报(理学版), 2012, 47(12): 41-46.
[9] 李映辉, 王守峰. 完全图的谱[J]. 长春师范大学学报, 2015, 34(6): 6-9.
[10] 李炯生, 查建国, 王新茂. 线性代数[M]. 合肥: 中国科学技术大学出版社, 2010.

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