LAUSR

For 0 ≤ α < 1, the Aα-spectral radius of a k-uniform hypergraph G is defined to be the spectral radius of the tensor Aα(G) := αD(G) + (1 − α)A(G), where D(G) and A(G) are diagonal and the adjacency tensors of G respectively. This paper presents several lower bounds for the difference between the Aα-spectral radius and an average degree km n for a connected k-uniform hypergraph with n vertices and m edges, which may be considered as the measures of irregularity of G. Moreover, two lower bounds on the Aα-spectral radius are obtained in terms of the maximum and minimum degrees of a hypergraph.