On the upper bounds of the perron roots of nonnegative matrices

An nxn matrix A = [aij] is nonnegative, (A ³ 0), if aij ³ 0 for 1 £ i, j £ n. The Perron root r(A) of A is a nonnegative eigenvalue of A satisfying r(A) ³ | l| for alleigenvalues of A. This article is devoted to establishing two different sequences of upper bounds for r(A).