The spectra of uniform hypertrees

In this paper we study the spectra of uniform hypertrees by using the generalized weighted incident matrix. We show that λ is a nonzero eigenvalue of the hypertree H corresponding to an eigenvector with all elements nonzero if and only if λ is a root of the polynomial φ(H)=∑i=0m(−1)i|Mi|x(m−i)r, where |Mi| is the number of matchings of order i in H.