Spectral radius of uniform hypergraphs

Abstract

We prove a result concerning the behavior of the spectral radius of a hypergraph under relocations of edges. We determine the unique hypergraphs with maximum spectral radius among connected k-uniform hypergraphs with fixed number of pendant edges, the unique k-uniform hypertrees with respectively maximum, second maximum and third maximum spectral radius, the unique k-uniform unicyclic hypergraphs (k-uniform linear unicyclic hypergraphs, respectively) with respectively maximum and second maximum spectral radius. We also determine the unique hypergraphs with maximum spectral radius among k-uniform unicyclic hypergraphs with given girth.