Resolution of the Symmetric Nonnegative Inverse Eigenvalue Problem for Matrices Subordinate to a Bipartite Graph

Abstract

There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues ?1=?2==?n if and only if, ?1 + ?n=0, ?2 + ?n-1=0,...,?m + ?n - m + 1=0, ?m + 1=0,...,?n - m=0, in which m is the matching numberof G. Other observations are also made about the symmetric nonnegative inverse eigenvalue problem with respect to a graph