BIMSA > Graphs: Structure, Spectra, and Extremes Graphs: Structure, Spectra, and Extremes Spectra of power hypergraph and its applications
Spectra of power hypergraph and its applications
Organizer
Shuliang Bai
Speaker
Lixiang Chen
Time
Thursday, August 27, 2026 4:00 PM - 5:00 PM
Venue
A3-4-101
Online
Zoom 293 812 9202 (BIMSA)
Abstract
A $k$-power hypergraph is constructed from a graph by adding $k-2$ new, edge-specific vertices to each edge, thereby turning every graph edge into a $k$-uniform hyperedge. This talk investigates the tensor spectra of power hypergraphs and their connections with signed graphs. We characterize their eigenvalues and algebraic multiplicities, relate the second-largest eigenvalue modulus to the weakest edges of the original graph, and introduce high-order spectra. These results reduce nonlinear tensor spectral problems to linear graph spectral problems and reveal structural information that may be invisible to the ordinary adjacency spectrum.
Speaker Intro
Lixiang Chen is an Associate Professor at Harbin Engineering University. He received his Ph.D. from Harbin Engineering University and conducted postdoctoral research at the Center for Combinatorics, Nankai University. His research interests include hypergraph spectral theory and discrete geometry. His work has appeared in journals including Advances in Applied Mathematics, Bulletin of the London Mathematical Society, and Journal of Combinatorial Theory, Series A.