Degree Type

Dissertation

Date of Award

2013

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Leslie Hogben

Second Advisor

Steven Butler

Abstract

We present an infinite example of trees cospectral with respect to the normalized Laplacian and a use of the weighted normalized Laplacian to find cospectral pairs of unweighted bipartite graphs with respect to the normalized Laplacian. We show that almost all trees are cospectral with respect to the normalized Laplacian. Further, we show that almost all trees are cospectral with respect to the generalized characteristic polynomial. This would imply that almost all trees T have a mate T' such that T and T' are simultaneously cospectral with respect to all of the adjacency, (signless) Laplacian, and normalized Laplacian matrices.

DOI

https://doi.org/10.31274/etd-180810-3522

Copyright Owner

Steven Osborne

Language

en

File Format

application/pdf

File Size

53 pages

Included in

Mathematics Commons

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