The α-spectral radius of general hypergraphs

Abstract 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 α with 0 ≤ α  α D ( H ) + ( 1 − α ) A ( H ) . First, we establish a upper bound on the α-spectral radius of connected irregular hypergraphs. Then we propose three local transformations of hypergraphs that increase the α-spectral radius. We also identify the unique hypertree with the largest α-spectral radius and the unique hypergraph with the largest α-spectral radius among hypergraphs of given number of pendent edges, and discuss the unique hypertrees with the next largest α-spectral radius and the unicyclic hypergraphs with the largest α-spectral radius.