On the signless Laplacian Estrada index of uniform hypergraphs

Abstract

Let H = (V, E) be a hypergraph and B its incidence matrix. Let Q(H) = BBT be the signless Laplacian matrix of H and λ1(Q), λ2(Q), …, λn(Q) are its eigenvalues. The signless Laplacian Estrada index of H is defined as italicSLEE()H=∑i=1neλi()Q 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.

The trace and Estrada index of uniform hypergraphs with cut vertices

“…One can refer [19] for a survey on Estrada index of graphs. We note here Lu et al [28] introduced the Estrada index of uniform hypergraphs by the signless Laplacian matrix of the hypergraphs.…”