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CLASSIFICATION OF TREES EACH OF WHOSE ASSOCIATED ACYCLIC MATRICES WITH DISTINCT DIAGONAL ENTRIES HAS DISTINCT EIGENVALUES

  • Published : 2008.02.29

Abstract

It is known that each eigenvalue of a real symmetric, irreducible, tridiagonal matrix has multiplicity 1. The graph of such a matrix is a path. In this paper, we extend the result by classifying those trees for which each of the associated acyclic matrices has distinct eigenvalues whenever the diagonal entries are distinct.

Keywords

acyclic matrix;Parter-vertex;simple eigenvalue

References

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Cited by

  1. The maximum number of P-vertices of some nonsingular double star matrices vol.313, pp.20, 2013, https://doi.org/10.1016/j.disc.2013.05.018
  2. Nonsingular acyclic matrices with full number of P-vertices vol.61, pp.1, 2013, https://doi.org/10.1080/03081087.2012.661425