Inverse Eigenvalue Problem for Laplacian Matrices of a Graph

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Abstract
For a given graph [Formula: see text], we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with [Formula: see text]. 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, regarding the minimum variance over a family of generalized Laplacian matrices with a size-normalized weighting.
Funding Information
  • National Science and Technology Council (NSTC-112-2628-M-110-003, NSTC-113-2115-M-110-010-MY3)
  • Natural Sciences and Engineering Research Council of Canada (RGPIN-2019-03934)
  • Pacific Institute for the Mathematical Sciences

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