To measure the degree of folding of a Protein, the definition of the Estrada index, EE G ðÞ= Pn i =1eλi was first proposed in [1], which widely used in biochemistry and complex networks [2–6].

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LU, Hongyan, XUE, Nini and ZHU, Zhongxun, 2021. On the signless Laplacian Estrada index of uniform hypergraphs. International Journal of Quantum Chemistry. 15 April 2021. Vol. 121, no. 8, p. e26579. DOI 10.1002/qua.26579. Abstract Let H = ( V , E ) be a hypergraph and B its incidence matrix. Let Q ( H ) = BB T be the signless Laplacian matrix of H and λ 1 ( Q ), λ 2 ( Q ), …, λ n ( Q ) are its eigenvalues. The signless Laplacian Estrada index of H is defined as which is first extended to hypergraph. We obtain lower and upper bounds for the index in terms of the number of vertices and edges of H . We also determine the unique graph with maximum SLEE among all k ‐uniform hypergraphs. In addition, we characterize the extremal hypertrees with the smallest and the largest SLEE among all k ‐uniform hypertrees.

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[2] E. Estrada, Bioinformatics 2002, 18, 697.

[3] E. Estrada, Proteins 2004, 54, 727.

[4] E. Estrada, N. Hatano, Chem. Phys. Lett. 2007, 439, 247.

[5] E. Estrada, J. A. Rodríguez-Valázquez, Phys. Rev. E 2005, 72(046105), 1.

[6] E. Estrada, J. A. Rodríguez-Valázquez, Phys. Rev. E 2005, 71(056103), 1.

For hypergraphs, a natural way to define the signless Laplacian Estrada index is to associate a hypergraph with its signless Laplacian matrix. It is worth mentioning that there is no natural extension record in the literature. Maybe the reason for this lack of results is the fact that Cooper and Dutle [9] proposed the study of hypergraphs via tensors in 2012, and this new approach has been widely accepted by researchers. However, it is high computational and theoretical cost to obtain eigenvalues of tensors and it does not seem natural to define the index of hypergraph by tensor, so we find that the study of hypergraphs through matrices still has its place. Indeed, Feng and Li [10] first attempt to study spectral theory of hypergraphs via matrices, and more authors pay attention to it, as in [11–13]. Kauê Cardoso and Vilmar Trevisan [14] define the energies of hypergraph by using matrices, they define the signless Laplacian matrix as Q(H)=BBT, B is incidence matrix of a hypergraph. Similar to ordinary graphs, we define the signless Laplacian Estrada index of hypergraphs as […]