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Mathematics > Combinatorics

arXiv:2411.00292 (math)
[Submitted on 1 Nov 2024 (v1), last revised 30 Nov 2024 (this version, v2)]

Title:Inverse eigenvalue problem for Laplacian matrices of a graph

Authors:Shaun Fallat, Himanshu Gupta, Jephian C.-H. Lin
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Abstract: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.
Subjects: Combinatorics (math.CO)
MSC classes: 05C50, 15A18, 15B57, 65F18
Cite as: arXiv:2411.00292 [math.CO]
  (or arXiv:2411.00292v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2411.00292

Submission history

From: Jephian C.-H. Lin [view email]
[v1] Fri, 1 Nov 2024 01:04:58 UTC (112 KB)
[v2] Sat, 30 Nov 2024 14:12:21 UTC (113 KB)
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