Inverse eigenvalue problem for Laplacian matrices of a graph
Combinatorics
2024-12-03 v2
Abstract
For a given graph , we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with . 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.
Cite
@article{arxiv.2411.00292,
title = {Inverse eigenvalue problem for Laplacian matrices of a graph},
author = {Shaun Fallat and Himanshu Gupta and Jephian C. -H. Lin},
journal= {arXiv preprint arXiv:2411.00292},
year = {2024}
}