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arXiv · 2411.00292

Inverse eigenvalue problem for Laplacian matrices of a graph

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.

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Shaun Fallat, Himanshu Gupta, Jephian C. -H. Lin. 2024-11-30. Inverse eigenvalue problem for Laplacian matrices of a graph. https://arxiv.org/abs/2411.00292

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