Inverse eigenvalue problem for Laplacian matrices of a graph

Fuente: arXiv
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Hauptverfasser: Fallat, Shaun, Gupta, Himanshu, Lin, Jephian C. -H.
Format: Preprint
Veröffentlicht: 2024
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author Fallat, Shaun
Gupta, Himanshu
Lin, Jephian C. -H.
author_facet Fallat, Shaun
Gupta, Himanshu
Lin, Jephian C. -H.
contents For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for certain families of graphs and graphs on a small number of vertices. Related considerations include studying the possible ordered multiplicity lists associated with stars and complete graphs and graphs with a few vertices. Finally, we present a novel investigation, both theoretically and numerically, the minimum variance over a family of generalized Laplacian matrices with a size-normalized weighting.
format Preprint
id arxiv_https___arxiv_org_abs_2411_00292
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Inverse eigenvalue problem for Laplacian matrices of a graph
Fallat, Shaun
Gupta, Himanshu
Lin, Jephian C. -H.
Combinatorics
05C50, 15A18, 15B57, 65F18
For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for certain families of graphs and graphs on a small number of vertices. Related considerations include studying the possible ordered multiplicity lists associated with stars and complete graphs and graphs with a few vertices. Finally, we present a novel investigation, both theoretically and numerically, the minimum variance over a family of generalized Laplacian matrices with a size-normalized weighting.
title Inverse eigenvalue problem for Laplacian matrices of a graph
topic Combinatorics
05C50, 15A18, 15B57, 65F18
url https://arxiv.org/abs/2411.00292