On the bisymmetric nonnegative inverse eigenvalue problem

The problem of finding conditions for a list of n complex numbers to be the eigenvalues of an n×n nonnegative matrix is called the nonnegative inverse eigenvalue problem (NIEP). The SNIEP (BNIEP) is the NIEP when the desired matrices are symmetric (bisymmetric). Recently, some sufficient conditions for the BNIEP are given by Julio and Soto in [6]. In this article, we study the BNIEP for n=4 and prove that the BNIEP and SNIEP are different for n=6. Then we give some sufficient conditions for the BNIEP and for the NIEP for normal centrosymmetric matrices related to the sufficient conditions of Julio and Soto and we also provide certain sufficient conditions for the BNIEP analogous to the sufficient conditions for the NIEP given by Borobia in [1]. Finally, we give sufficient conditions for the BNIEP when the prescribed diagonal entries are required.