On the Laplacian and Signless Laplacian Characteristic Polynomials of a Digraph

Hilal Ahmad Ganie, Yilun Shang

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Article number52
JournalSymmetry
Volume15
Issue number1
DOIs
Publication statusPublished - 25 Dec 2022

Fingerprint

Dive into the research topics of 'On the Laplacian and Signless Laplacian Characteristic Polynomials of a Digraph'. Together they form a unique fingerprint.

Cite this