Graph Laplacians with Higher Accuracy

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Yoon, Mary
Format: Preprint
Veröffentlicht: 2025
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866908306532990976
author Yoon, Mary
author_facet Yoon, Mary
contents Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we show that the number of graphs having cospectral mates with these matrices is significantly less than the ones with other known matrices. We also investigate their spectral properties and explicitly compute their eigenvalues and eigenvectors for some graphs. Along the line, we also prove the existence of a weighted signed graph with given Laplacian eigenvalues.
format Preprint
id arxiv_https___arxiv_org_abs_2504_04461
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Graph Laplacians with Higher Accuracy
Yoon, Mary
Combinatorics
05C50, 05C22, 15A18, 15B99
Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we show that the number of graphs having cospectral mates with these matrices is significantly less than the ones with other known matrices. We also investigate their spectral properties and explicitly compute their eigenvalues and eigenvectors for some graphs. Along the line, we also prove the existence of a weighted signed graph with given Laplacian eigenvalues.
title Graph Laplacians with Higher Accuracy
topic Combinatorics
05C50, 05C22, 15A18, 15B99
url https://arxiv.org/abs/2504.04461