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

• Published : 2008.02.29
• 40 4

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

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2. Nonsingular acyclic matrices with full number of P-vertices vol.61, pp.1, 2013, https://doi.org/10.1080/03081087.2012.661425