Lower bounds for the [formula omitted]-spectral radius of uniform hypergraphs

Abstract

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 the diagonal and adjacency tensors of G, respectively. This paper presents several lower bounds for the difference between the Aα-spectral radius and an average degree kmn of a connected k-uniform hypergraph G with n vertices and m edges, which are considered as 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 uniform hypergraphs.