Elsevier, Linear Algebra and its Applications, 2(434), p. 514-525, 2011
DOI: 10.1016/j.laa.2010.09.017
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We provide positive answers to some open questions presented recently by Kim and Shader on a continuity-like property of the P-vertices of nonsingular matrices whose graph is a path. A criterion for matrices associated with more general trees to have at most n − 1 P-vertices is established. The cases of the cycles and stars are also analyzed. Several algorithms for generating matrices with a given number of P-vertices are proposed.