3 papers
math.CO2025
The Weak Version of the Graph Complement Conjecture and Partial Results for the Delta Conjecture
Francesco Barioli, Shaun M. Fallat, Himanshu Gupta +1
Since the transformative workshop by the American Institute of Mathematics on the minimum rank of a graph, two longstanding open problems have captivated the community interested i…
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…