Estrada index of hypergraphs via eigenvalues of tensors

Abstract

A uniform hypergraph H is corresponding to an adjacency tensor A H . We define an Estrada index of H by using all the eigenvalues λ 1 , . . . , λ k of A H as k i=1 e λi . 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.

The trace and Estrada index of uniform hypergraphs with cut vertices

“…Recently Clark and Cooper [5] generalized the Harary-Sachs theorem of graphs to uniform hypergraphs by using Veblen hypergraphs. Sun-Zhou-Bu [33] generalized the Estrada index of graphs to uniform hypergraphs, which is closely related to the traces of the adjacency tensor. Definition 1.1 ([33]).…”

Signless Laplacian Estrada index and Laplacian Estrada index of uniform hypergraphs

“…In 2021, Sun, Zhou and Bu [27] generalized the definition of the Estrada index to uniform hypergraphs and obtained some bounds for it. Moreover, they studied the Estrada indices of some specific r-uniform hypergraphs.…”

“…In this paper, motivated by [19,27], we introduce the signless Laplacian Estrada index SLEE(H) and the Laplacian Estrada index LEE(H) of an r-uniform hypergraph H. We also obtain an order r + 1 trace formula of the (signless) Laplacian tensor of H. Further, we establish some bounds on SLEE(H) and LEE(H). In general, the problem of finding good bounds is hindered by the fact that eigenvalues of hypergraphs may be nonreal.…”