• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.95-99
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• 2008

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.