Signless Laplacian Estrada index and Laplacian Estrada index of uniform hypergraphs

TL;DR

This paper extends the concepts of Laplacian and signless Laplacian Estrada indices to uniform hypergraphs, deriving trace formulas and bounds that deepen understanding of their spectral properties.

Contribution

It introduces a trace formula for the (signless) Laplacian tensor of uniform hypergraphs and establishes bounds for their Estrada indices and related spectral measures.

Findings

Derived an order r+1 trace formula for the (signless) Laplacian tensor.

Established bounds for the signless Laplacian Estrada index.

Provided a bound involving both Laplacian Estrada index and Laplacian energy.

Abstract

We generalize the notions of Laplacian and signless Laplacian Estrada index to uniform hypergraphs. For an $r$-uniform hypergraph $H,$ we derive an order $r+1$ trace formula of the (signless) Laplacian tensor of $H.$ Among others by using this trace formula, we obtain lower bounds for the signless Laplacian Estrada index and upper bounds for the Laplacian Estrada index. Moreover, we establish a bound involving both the Laplacian Estrada index and Laplacian energy of a uniform hypergraph.