TY - JOUR

T1 - Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars

AU - Johnson, Charles R.

AU - Leal-Duarte, António

AU - Saiago, Carlos Manuel

N1 - 1- This research was supported by Centro de Matemática da Universidade de Coimbra. 2- Research supported in part by Fundação para a Ciência e a Tecnologia, Portugal, through the research grant SFRH/BD/899/2000. Part of the research was done while visiting the College of William and Mary.

PY - 2003/11/1

Y1 - 2003/11/1

N2 - We characterize the possible lists of orderedmultiplicities among matrices whose graph is a generalized star (a tree in which atmost one vertex has degree greater than 2) or a double generalized star. Here, the inverse eigenvalue problem (IEP) for symmetric matrices whose graph is a generalized star is settled. The answer is consistent with a conjecture that determination of the possible orderedmultiplicities is equivalent to the IEP for a given tree. Moreover, a key spectral feature of the IEP in the case of generalized stars is shown to characterize them among trees.

AB - We characterize the possible lists of orderedmultiplicities among matrices whose graph is a generalized star (a tree in which atmost one vertex has degree greater than 2) or a double generalized star. Here, the inverse eigenvalue problem (IEP) for symmetric matrices whose graph is a generalized star is settled. The answer is consistent with a conjecture that determination of the possible orderedmultiplicities is equivalent to the IEP for a given tree. Moreover, a key spectral feature of the IEP in the case of generalized stars is shown to characterize them among trees.

KW - Hermitian matrices

KW - Eigenvalues

KW - Multiplicities

KW - Trees

KW - Inverse eigenvalue problems

U2 - 10.1016/S0024-3795(03)00582-2

DO - 10.1016/S0024-3795(03)00582-2

M3 - Conference article

SN - 0024-3795

VL - 373

SP - 311

EP - 330

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - Suppl.

T2 - Conference on Combinatorial Matrix Theory

Y2 - 14 January 2002 through 17 January 2002

ER -