abs_vol18_pp442-461. 26KB Jun 04 2011 12:05:47 AM

ELA

ON THE INVERSE EIGENVALUE PROBLEMS: THE CASE OF

SUPERSTARS

∗

ROS ´ARIO FERNANDES†

Abstract. Let T _{be a tree and let}x0 be a vertex ofT. T is called a superstar with central

vertexx0ifT₋x0is a union of paths. The General Inverse Eigenvalue Problem for certain trees is

partially answered. Using this description, some superstars are presented for which the problem of ordered multiplicity lists and the Inverse Eigenvalue Problem are not equivalent.

Key words. Eigenvalues, Tree, Graph, Symmetric matrices.

AMS subject classifications.15A18, 05C38, 05C50.

∗_{Received by the editors September 16, 2007. Accepted for publication July 27, 2009. Handling}

Editor: Stephen J. Kirkland.

†_{Departamento de Matem´atica, Faculdade de Ciˆencias e Tecnologia, Universidade Nova de Lisboa,}

Quinta da Torre, 2829-516 Caparica, Portugal (mrff@fct.unl.pt). This research was done within the activities of “Centro de Estruturas Lineares e Combinat´orias”.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 442-461, August 2009