The algebraic multiplicity of the spectral radius of a hypertree

It is well-known that the spectral radius of a connected uniform hypergraph is an eigenvalue of the hypergraph. However, its algebraic multiplicity remains unknown. In this paper, we use the Poisson Formula and matching polynomials to determine the algebraic multiplicity of the spectral radius of a uniform hypertree

Estrada index of hypergraphs via eigenvalues of tensors

A uniform hypergraph $\mathcal{H}$ is corresponding to an adjacency tensor $\mathcal{A}_\mathcal{H}$. We define an Estrada index of $\mathcal{H}$ by using all the eigenvalues $\lambda_1,\dots,\lambda_k$ of $\mathcal{A}_\mathcal{H}$ as $\sum_{i=1}^k e^{\lambda_i}$. The bounds for the Estrada indices of uniform hypergraphs are given. And we characterize the Estrada indices of $m$-uniform hypergraphs whose spectra of the adjacency tensors are $m$-symmetric. Specially, we characterize the Estrada indices of uniform hyperstars