Inverse eigenvalue problem for Laplacian matrices of a graph

2024/11/01 by Fallat, Shaun, Gupta, Himanshu, Lin, Jephian C. -H. · 1 citation
#05C50 #15A18 #15B57 #65F18 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.00292

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.

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• Inverse eigenvalue problem for discrete Schrödinger operators of a graph

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