Estrada index of hypergraphs via eigenvalues of tensors

Abstract

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