The weighted hypergraph with the maximum spectral radius

Let Γn,k,a and Un,k,a denote respectively the classes of weighted k-uniform hypertrees and connected weighted k-uniform linear and nonlinear unicyclic hypergraphs of order n with the positive integer weights and the fixed total weight sum a, where n, k (k≥3), and a are positive integers with a≥n−1k−1≥2 for Γn,k,a while a≥nk−1≥2 for Un,k,a. Four new and useful operations are proposed for comparing the spectral radii of the weighted hypergraphs under consideration. The weighted hypergraphs having the maximum spectral radii among Γn,k,a and Un,k,a are characterized.