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On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem. / Buslov, V.A.

In: Journal of Mathematical Sciences, Vol. February 2016, Volume 212, No. Issue 6, 2016, p. 643-653.

Research output: Contribution to journal › Article › peer-review

Harvard

Buslov, VA 2016, 'On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem', Journal of Mathematical Sciences, vol. February 2016, Volume 212, no. Issue 6, pp. 643-653. <http://link.springer.com/article/10.1007/s10958-016-2695-3>

APA

Buslov, V. A. (2016). On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem. Journal of Mathematical Sciences, February 2016, Volume 212(Issue 6), 643-653. http://link.springer.com/article/10.1007/s10958-016-2695-3

Vancouver

Buslov VA. On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem. Journal of Mathematical Sciences. 2016;February 2016, Volume 212(Issue 6):643-653.

Author

Buslov, V.A. / On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem. In: Journal of Mathematical Sciences. 2016 ; Vol. February 2016, Volume 212, No. Issue 6. pp. 643-653.

BibTeX

@article{16f0d9f3280149a4aa2f989fef128b09,
title = "On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem",
abstract = "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.",
keywords = "Laplace Matrix, Weighted Digraph, Span Forest, Constant Sign",
author = "V.A. Buslov",
year = "2016",
language = "English",
volume = "February 2016, Volume 212",
pages = "643--653",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "Issue 6",

}

RIS

TY - JOUR

T1 - On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem

AU - Buslov, V.A.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Laplace Matrix

KW - Weighted Digraph

KW - Span Forest

KW - Constant Sign

M3 - Article

VL - February 2016, Volume 212

SP - 643

EP - 653

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - Issue 6

ER -

ID: 7552396