We show that $\lambda$ is an eigenvalue of a $k$-uniform hypertree $(k \geq 3)$ 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.
@article{10_37236_7442,
author = {Gregory J. Clark and Joshua N. Cooper},
title = {On the adjacency spectra of hypertrees},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {2},
doi = {10.37236/7442},
zbl = {1391.15082},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7442/}
}
TY - JOUR
AU - Gregory J. Clark
AU - Joshua N. Cooper
TI - On the adjacency spectra of hypertrees
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/7442/
DO - 10.37236/7442
ID - 10_37236_7442
ER -
%0 Journal Article
%A Gregory J. Clark
%A Joshua N. Cooper
%T On the adjacency spectra of hypertrees
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/7442/
%R 10.37236/7442
%F 10_37236_7442
Gregory J. Clark; Joshua N. Cooper. On the adjacency spectra of hypertrees. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7442
