On the Laplacian and Signless Laplacian Characteristic Polynomials of a Digraph

Autor:	Hilal A. Ganie, Yilun Shang
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	digraphs adjacency matrix (spectrum) (signless) Laplacian matrix (spectrum) (signless) Laplacian coefficients Mathematics QA1-939
Zdroj:	Symmetry, Vol 15, Iss 1, p 52 (2022)
Druh dokumentu:	article
ISSN:	2073-8994
DOI:	10.3390/sym15010052
Popis:	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.
Databáze:	Directory of Open Access Journals
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