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Nonsingular acyclic matrices with full number of P-vertices
(Linear & Multilinear Algebra, 2013)
We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In particular, we show that such trees have an even number of vertices. Both results provide answers to questions proposed by ...
Unordered multiplicity lists of wide double paths
(DMFA Slovenije, 2013)
Recently, Kim and Shader analyzed the multiplicities of the eigenvalues of a Φ-binary tree. We carry this discussion forward extending their results to a larger family of trees, namely, the wide double path, a tree consisting ...