2017/11/04 by Gregory J. Clark, Joshua Cooper, Clark, Gregory J. +1
Mathematics · #FOS: Mathematics #Spectral Theory (math.SP) #math.SP
paper · pdf · doi:10.48550/arxiv.1711.01466
arxiv created 2017/11/04 · arxiv updated 2017/11/07
We extend the results of Zhang et al. to 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.