The α-spectral radius of general hypergraphs

Given a hypergraph H of order n with rank k >= 2, denote by D(H) and A(H) the degree diagonal tensor and the adjacency tensor of H , respectively, of order k and dimension n . For real number alpha with 0 <= alpha <= 1, the alpha-spectral radius of H is defined to be the spectral radius of the symmetric tensor alpha D(H) + (1 - alpha)A(H). First, we establish a upper bound on the alpha-spectral radius of connected irregular hypergraphs. Then we propose three local trans-formations of hypergraphs that increase the alpha-spectral radius. We also identify the unique hypertree with the largest alpha-spectral radius and the unique hypergraph with the largest alpha-spectral radius among hypergraphs of given number of pendent edges, and discuss the unique hypertrees with the next largest alpha-spectral radius and the unicyclic hypergraphs with the largest alpha-spectral radius. (C) 2020 Elsevier Inc. All rights reserved.