## Adjacency Spectra of Hypertrees and other Hypergraphs with Few Eigenvalues

- Dec. 8, 2017
- 2:30 p.m.
- LeConte 310

## Abstract

We show how, if a complete set of adjacency eigenvalues (without multiplicity) is known, one can compute the full characteristic polynomial by combining expressions for its coefficients in terms of subgraph counts with the Vieta formulas. As an application, using a strengthened version of a recent result of Zhang-Kang-Shan-Bai, we obtain the complete list of eigenvalues of a hypertree and then use this technique to extract their multiplicities. This also leads to a spectral characterization of power trees and several open questions.

Joint work with Greg Clark of the University of South Carolina.