On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem
- 作者: Buslov V.A.1
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隶属关系:
- St.Petersburg State University
- 期: 卷 212, 编号 6 (2016)
- 页面: 643-653
- 栏目: Article
- URL: https://bakhtiniada.ru/1072-3374/article/view/237118
- DOI: https://doi.org/10.1007/s10958-016-2695-3
- ID: 237118
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详细
Let L be the Laplace matrix of a weighted digraph. The aim of the paper is to establish a simple way for computing any coefficient of the characteristic polynomial of L as a constant sign sum over the incoming spanning forests. The idea is to express L as the product of generalized (weighted) incidence matrices. It turns out that the minors of them can be studied in terms of the tree-like structure of the digraph. This makes it possible to compute the minors of L.
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