Brauer Upper Bound for the Z-Spectral Radius of Nonnegative Tensors

摘要

In this paper,we have proposed an upper bound for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor,which is called the Brauer upper bound:ρz(A) ≤ 1/2 maxi,j∈N j≠i (ai…i+aj…j+√(ai…i-aj…j)2+4ri(A)rj(A)),where ri(A) =Σii2…im≠ii…i aii2…im,i,i2,…,im ∈ N ={1,2,…,n}.As applications,a bound on the Z-spectral radius of uniform hypergraphs is presented.