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.