Classification of trees each of whose associated acyclic matrices with distinct diagonal entries has distinct eigenvalues
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 95-99 Printed March 1, 2008
In-Jae Kim and Bryan L. Shader Minnesota State University and University of Wyoming
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.