Nonsingular acyclic matrices with full number of P-vertices
Milica Anđelić, Aleksandra Erić, Carlos M. da Fonseca · Linear and Multilinear Algebra · 2012
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 Kim and Shader. In the end, related classifications on nonsingular trees with the size of a P-set bounded are addressed.