On the Adjacency Spectra of Hypertrees

Author(s)

Gregory J. Clark
Joshua N. Cooper, University of South CarolinaFollow

Document Type

Article

Abstract

We show that λ is an eigenvalue of a k-uniform hypertree (k ≥ 3) if and only if it is a root of a particular matching polynomial for a connected induced subtree. We then use this to provide a spectral characterization for power hypertrees. Notably, the situation is quite different from that of ordinary trees, i.e., 2-uniform trees. We conclude by presenting an example (an 11 vertex, 3-uniform non-power hypertree) illustrating these phenomena.

Digital Object Identifier (DOI)

https://doi.org/10.37236/7442

Publication Info

Published in Electronic Journal of Combinatorics, Volume 25, Issue 2, 2018.

APA Citation

Clark, G. J., & Cooper, J. N. (2018). On the Adjacency Spectra of Hypertrees. The Electronic Journal of Combinatorics, 25(2).https://doi.org/10.37236/7442

Rights

©The authors. Released under the (CC BY-ND licenseInternational 4.0).