5 papers · 1 filter
Burning Signed Graphs
Shaun Fallat, Himanshu Gupta, Kamyar Khodamoradi +1
We introduce and analyze a new model of graph burning, in which two competing fires (coloured yellow and green) ignite vertices of a given signed graph and propagate along its edge…
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…
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…
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…
Sufficient conditions for total positivity, compounds, and Dodgson condensation
Shaun Fallat, Himanshu Gupta, Charles R. Johnson
A -by- matrix is called totally positive () if all its minors are positive and if all of its -by- submatrices are . For an arbitrary totally positive mat…