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


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Abstract

There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues λ1≥λ2≥…≥λn if and only if, λ1 + λn≥0, λ2 + λn-1≥0,…, λm + λnm + 1≥0, λm + 1≥0,…,λnm≥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

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