Signless Laplacian Estrada index and Laplacian Estrada index of uniform hypergraphs

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.