Determinant of the Laplacian Matrix of a Weighted Directed Graph

Debajit Kalita ()
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Debajit Kalita: Tezpur University, Department of Mathematical Sciences

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 57-62 from Springer

Abstract: Abstract The notion of weighted directed graph is a generalization of mixed graphs. In this article a formula for the determinant of the Laplacian matrix of a weighted directed graph is obtained. It is a generalization of the formula for the determinant of the Laplacian matrix of a mixed graph obtained by Bapat et al. (Linear Multilinear Algebra 46:299–312, 1999).

Keywords: Laplacian matrix; Mixed graph; Weighted directed graph; 3-Colored digraph; Essential spanning subgraph; 05C50; 05C05; 15A18 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1053-5_5

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DOI: 10.1007/978-81-322-1053-5_5

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