A bound on the spectral radius of hypergraphs with e edges

For r >= 3, let f(r): [0, infinity) -> [1, infinity) be the unique analytic function such that f(r)(((k)(r)) = ((k-1)(r-1)) for any k >= r - 1. We prove that the spectral radius of an r-uniform hypergraph H with e edges is at most f(r)(e). The equality holds if and only if e = ((k)(r)) for some positive integer k and H is the union of a complete r-uniform hypergraph K-k(r) and some possible isolated vertices. This result generalizes the classical Stanley's theorem on graphs. (C) 2018 Elsevier Inc. All rights reserved.