On the signless Laplacian Estrada index of uniform hypergraphs

摘要

Let H = (V, E) be a hypergraph and B its incidence matrix. Let Q(H) = BBT be the signless Laplacian matrix of H and lambda(1)(Q), lambda(2)(Q), horizontal ellipsis , lambda(n)(Q) are its eigenvalues. The signless Laplacian Estrada index of H is defined as SLEE(H) n-ary sumation i=1ne lambda i(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.