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发表于 2025-3-21 19:58:48 | 显示全部楼层 |阅读模式
书目名称Graphs and Matrices
编辑Ravindra B. Bapat
视频video
丛书名称Universitext
图书封面Titlebook: ;
出版日期Textbook 2014Latest edition
版次2
doihttps://doi.org/10.1007/978-1-4471-6569-9
isbn_softcover978-1-4471-6568-2
isbn_ebook978-1-4471-6569-9Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
The information of publication is updating

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发表于 2025-3-21 21:29:58 | 显示全部楼层
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发表于 2025-3-22 08:28:04 | 显示全部楼层
Themenhefte Schwerpunktprogramm Umweltted. The Matrix-Tree Theorem and some related results are proved. Bounds for the Laplacian spectral radius are obtained. The edge-Laplacian is considered and a formula for the inverse of the edge-Laplacian of a tree is obtained. In the process we also obtain a formula for the Moore-Penrose inverse of the incdence matrix of a tree.
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发表于 2025-3-22 16:24:56 | 显示全部楼层
https://doi.org/10.1007/978-3-662-58390-6 a partitioned matrix and Cauchy–Binet formula. Important properties of eigenvalues of symmetric matrices, including Spectral Theorem and Interlacing Theorem are reviewed. Basic notions of generalized inverses, including Moore–Penrose inverse are stated. Relevant concepts and results are given, although we omit the proofs.
发表于 2025-3-22 18:56:29 | 显示全部楼层
https://doi.org/10.1007/978-3-663-12252-4l matrices. The interplay between the two matrices and the incidence matrix is considered in detail. Minors of the fundamental matrices are described in terms of the graph. Some of the results appear in print form for the first time. The development in this chapter is different than that found in most texts.
发表于 2025-3-22 22:53:40 | 显示全部楼层
Mutagenesis in Sub-Mammalian Systemsthe line graph of a tree and those of the Laplacian as well as the signless Laplacian are shown to be related to each other. This connection is exploited to obtain several statements centered around the classical result that the nullity of the line graph of a tree is at most one.
发表于 2025-3-23 02:35:55 | 显示全部楼层
发表于 2025-3-23 08:25:56 | 显示全部楼层
https://doi.org/10.1007/978-981-16-9720-3n detail. We first illustrate the concept of matrix completion by considering the nonsingular completion problem. We then introduce the preliminaries on chordal graphs. Then we prove the main result that a graph is positive definite completable if and only if it is chordal.
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