Construction of Real Skew-Symmetric Matrices from Interlaced Spectral Data, and Graph

Document Type

Article

Publication Date

4-2015

Abstract

A 1989 result of Duarte asserts that for a given tree T on n vertices, a fixed vertex i, and two sets of distinct real numbers L, M of sizes n – 1, respectively, such that M strictly interlaces L, there is a real symmetric matrix A such that graph of A is T, eigenvalues of A are given by L, and eigenvalues of A(i) are given by M. In 2013, a similar result for connected graphs was published by Hassani Monfared and Shader, using the Jacobian method. Analogues of these results are presented here for real skew-symmetric matrices whose graphs belong to a certain family of trees, and all of their supergraphs.

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