The Strong Spectral Property and the Inverse Eigenvalue Problem for Graphs
Start Date
August 2025
End Date
August 2025
Location
ALT 304
Abstract
The Inverse Eigenvalue Problem on Graphs aims to establish the connection between a graph and all possible eigenvalues of matrices that are associated with the graph. For a given matrix, its spectrum is the multiset consisting of all its eigenvalues. We explore how a new tool called the Strong Spectral Property (SSP) can be utilized to obtain a deeper understanding of the relations between the spectra of matrices with a given graph and the spectra of matrices in supergraphs of the graph. Specifically, we apply the definition of the SSP to different graph families in order to see which graphs have matrices that always have the SSP, or what constraints are necessary for a graph to have matrices that have the SSP.
The Strong Spectral Property and the Inverse Eigenvalue Problem for Graphs
ALT 304
The Inverse Eigenvalue Problem on Graphs aims to establish the connection between a graph and all possible eigenvalues of matrices that are associated with the graph. For a given matrix, its spectrum is the multiset consisting of all its eigenvalues. We explore how a new tool called the Strong Spectral Property (SSP) can be utilized to obtain a deeper understanding of the relations between the spectra of matrices with a given graph and the spectra of matrices in supergraphs of the graph. Specifically, we apply the definition of the SSP to different graph families in order to see which graphs have matrices that always have the SSP, or what constraints are necessary for a graph to have matrices that have the SSP.
