Lower bounds for the Aα-spectral radius of uniform hypergraphs

For 0 <= alpha < 1, the A(alpha)-spectral radius of a k-uniform hypergraph Gis defined to be the spectral radius of the tensor A(alpha)(G) := alpha D(G) +(1 - alpha)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(alpha)-spectral radius and an average degree km/n of a connected k-uniform hypergraph Gwith nvertices and medges, which are considered as measures of irregularity of G. Moreover, two lower bounds on the A(alpha)-spectral radius are obtained in terms of the maximum and minimum degrees of uniform hypergraphs. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper presents lower bounds for the difference between the A(alpha)-spectral radius and the irregularity measures of connected k-uniform hypergraphs, as well as two lower bounds on the A(alpha)-spectral radius in terms of the maximum and minimum degrees of uniform hypergraphs.