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.
|Number of pages||20|
|Journal||Linear Algebra and Its Applications|
|Publication status||Published - 1 Nov 2003|
|Event||Conference on Combinatorial Matrix Theory - Pohang, Korea, Republic of|
Duration: 14 Jan 2002 → 17 Jan 2002
- Hermitian matrices
- Inverse eigenvalue problems