Geodesic
On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices
The electronic journal of linear algebra, Tome 11 (2004), pp. 41-50.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For a given acyclic graph G, an important problem is to characterize all of the eigenvalues over all symmetric matrices with graph G. Of particular interest is the connection between this standard inverse eigenvalue problem and describing all the possible associated ordered multiplicity lists, along with determining the minimum number of distinct eigenvalues for a symmetric matrix with graph G. In this note two important open questions along these lines are resolved, both in the negative.
Classification : 15A18, 15A48, 05C50
Keywords: symmetric matrices, acyclic matrices, eigenvalues, graphs, binary trees 
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     author = {Barioli, Franceso and Fallat, Shaun M.},
     title = {On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices},
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Barioli, Franceso; Fallat, Shaun M. On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices. The electronic journal of linear algebra, Tome 11 (2004), pp. 41-50. http://geodesic.mathdoc.fr/item/ELA_2004__11__a18/