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

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For 0 ≤ α < 1 , the A α -spectral radius of a k -uniform hypergraph G is defined to be the spectral radius of the tensor A α ( G ) : = α D ( 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 A α -spectral radius and an average degree k m n 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 A α -spectral radius are obtained in terms of the maximum and minimum degrees of uniform hypergraphs.