3 papers
math.CO2026
The Strong Spectral Property and the Jacobian Method for Weighted Laplacian Matrices
Minerva Catral, Shaun Fallat, Himanshu Gupta +1
Strong matrix properties, roughly speaking, refer to generic conditions on a matrix such that its spectral perturbation and pattern perturbation interact nicely to cover a neighbor…
math.CO2024
Inverse eigenvalue problem for Laplacian matrices of a graph
Shaun Fallat, Himanshu Gupta, Jephian C. -H. Lin
For a given graph , we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with . This new…
math.CO2024
Minimum number of distinct eigenvalues of distance-regular and signed Johnson graphs
Shaun Fallat, Himanshu Gupta, Allen Herman +1
We study the minimum number of distinct eigenvalues over a collection of matrices associated with a graph. Lower bounds are derived based on the existence or non-existence of certa…