The α-normal labelling method for computing the p-spectral radii of uniform hypergraphs.

Let G be an r-uniform hypergraph of order n. For each p ≥ 1 , the p-spectral radius λ (p) (G) is defined as λ (p) (G) := max | x 1 | p + ⋯ + | x n | p = 1 r ∑ { i 1 , ... , i r } ∈ E (G) x i 1 ⋯ x i r . The p-spectral radius was introduced by Keevash-Lenz-Mubayi, and subsequently studied by Nikiforov in 2014. The most extensively studied case is when p = r, and λ (r) (G) is called the spectral radius of G. The α-normal labelling method, which was introduced by Lu and Man in 2014, is effective method for computing the spectral radii of uniform hypergraphs. It labels each corner of an edge by a positive number so that the sum of the corner labels at any vertex is 1 while the product of all corner labels at any edge is α. Since then, this method has been used by many researchers in studying λ (r) (G). In this paper, we extend Lu and Man's α-normal labelling method to the p-spectral radii of uniform hypergraphs for p ≠ r ; and find some applications. [ABSTRACT FROM AUTHOR]