Resolution of the symmetric nonnegative inverse eigenvalue problem for matrices subordinate to a bipartite graph

There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues lambda(1)greater than or equal tolambda(2)greater than or equal to...greater than or equal to(n) if and only if lambda(1) + lambda(n) greater than or equal to 0, lambda(2) + lambda(n-1) greater than or equal to 0,..., lambda(m) + lambda(n-m+1) greater than or equal to 0, lambda(m+1)greater than or equal to0,...,lambda(n-m) greater than or equal to 0, in which m is the matching number of G. Other observations are also made about the symmetric nonnegative inverse eigenvalue problem with respect to a graph.