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).
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References
Bapat, R.B., Kalita, D., Pati, S.: On weighted directed graphs. Linear Algebra Appl. 436, 99–111 (2012)
Bapat, R.B., Grossman, J.W., Kulkarni, D.M.: Generalized matrix tree theorem for mixed graphs. Linear Multilinear Algebra 46, 299–312 (1999)
Marcus, M., Minc, H.: Survey of Matrix Theory and Matrix Inequalities. Allyan and Bacon, Boston (1964)
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The author sincerely thanks the referee for a careful reading of this manuscript and valuable suggestions.
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Kalita, D. (2013). Determinant of the Laplacian Matrix of a Weighted Directed Graph. In: Bapat, R., Kirkland, S., Prasad, K., Puntanen, S. (eds) Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer, India. https://doi.org/10.1007/978-81-322-1053-5_5
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DOI: https://doi.org/10.1007/978-81-322-1053-5_5
Publisher Name: Springer, India
Print ISBN: 978-81-322-1052-8
Online ISBN: 978-81-322-1053-5
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