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.
Keywords:Graphs / Matrices / Eigenvalues / Double stars / P-vertices
Source:Discrete Mathematics, 2013, 313, 20, 2192-2194
- Elsevier B.V.