The maximum number of P-vertices of some nonsingular double star matrices
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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 Kim and Shader regarding the trees for which each
nonsingular matrix has at most n − 2 P-vertices.