Show simple item record

dc.contributor.advisor Forman, Robin
dc.creatorMcIlwain, Mary Hope
dc.date.accessioned 2009-06-04T07:59:19Z
dc.date.available 2009-06-04T07:59:19Z
dc.date.issued 1998
dc.identifier.urihttps://hdl.handle.net/1911/19288
dc.description.abstract Let G be a simple graph with n vertices. We define a Laplacian $\Delta$ on G which depends on an assignment of a weight to each vertex of G. One of the eigenvalues of $\Delta$ will always be 0. We fix the remaining (n $-$ 1) eigenvalues and ask for which graphs we can find a set of weights which generate a Laplacian with the spectrum $\Lambda.$ We demonstrate that it is always possible to solve the inverse spectral problem for a three vertex graph. In the case of $K\sb4$, the complete graph on four vertices, we prove several results. First, we give two proofs that it is always possible to solve the inverse problem. In addition, we give a description of all possible solution spaces for the inverse spectral problem. We also demonstrate that if we choose the eigenvalues to be positive it is not always possible to solve the inverse spectral problem with a set of positive weights.
dc.format.extent 76 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title Can you hear the size of the vertices? An inverse spectral problem of Laplacians on weighted graphs
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation McIlwain, Mary Hope. "Can you hear the size of the vertices? An inverse spectral problem of Laplacians on weighted graphs." (1998) Diss., Rice University. https://hdl.handle.net/1911/19288.


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record