Nonsingular acyclic matrices with an extremal number of P-vertices

作者：Du Zhibin; da Fonseca C M^*

来源：Linear Algebra and Its Applications, 2014, 442: 2-19.

DOI：10.1016/j.laa.2013.01.010

• Trees
• Nonsingular acyclic matrices
• Eigenvalue multiplicities
• P-vertices

It is known that for any nonsingular acyclic matrix of order n, the maximum number of P-vertices is n if n is even, and n-1 if n is odd. In this paper, we thoroughly characterize the trees where those bounds are achieved. In addition, for those trees and for any nonnegative integer k less than or equal to the extremal number of P-vertices, we provide an algorithm to construct a nonsingular matrix whose graph is the given tree and the number of P-vertices is k. Illustrative examples are given.

• 出版日期2014-2-1
• 单位同济大学