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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 ...
The maximum number of P-vertices of some nonsingular double star matrices
(Elsevier B.V., 2013)
In this short note, we construct a nonsingular matrix A whose graph is a double star of order n >= 4 with n - 2 P-vertices. This example leads to a positive answer, for n >= 6, to a last open question proposed recently by ...