On the Laplacian and Signless Laplacian Characteristic Polynomials of a Digraph

Ganie, Hilal A. and Shang, Yilun (2022) On the Laplacian and Signless Laplacian Characteristic Polynomials of a Digraph. Symmetry, 15 (1). p. 52. ISSN 2073-8994

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Official URL: https://doi.org/10.3390/sym15010052


Let D be a digraph with n vertices and a arcs. The Laplacian and the signless Laplacian matrices of D are, respectively, defined as L(D)=Deg+(D)−A(D) and Q(D)=Deg+(D)+A(D), where A(D) represents the adjacency matrix and Deg+(D) represents the diagonal matrix whose diagonal elements are the out-degrees of the vertices in D. We derive a combinatorial representation regarding the first few coefficients of the (signless) Laplacian characteristic polynomial of D. We provide concrete directed motifs to highlight some applications and implications of our results. The paper is concluded with digraph examples demonstrating detailed calculations.

Item Type: Article
Uncontrolled Keywords: digraphs; adjacency matrix (spectrum); (signless) Laplacian matrix (spectrum); (signless) Laplacian coefficients
Subjects: G400 Computer Science
G500 Information Systems
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 03 Jan 2023 16:53
Last Modified: 03 Jan 2023 17:00
URI: https://nrl.northumbria.ac.uk/id/eprint/51034

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