Dissertation
Applications of Generalized Laplacian Matrices in Graph Tiling
Doctor of Philosophy (PhD), Washington State University
01/2014
Handle:
https://hdl.handle.net/2376/5202
Abstract
This dissertation is an examination of how generalized Laplacian matrices (in particular, their determinants) may be useful in determining graph tilings. Since there is a very strong connection between the generalized Laplacian matrix of a graph and the edge deletion polynomial (also known as the tiling polynomial) of a graph, this paper will determine edge deletion polynomials (instead of generalized Laplacian matrices) for specific graph types. Some types will be approached from more of a linear algebra standpoint, while others will be calculated directly via a more combinatorial approach (and some types will have the edge deletion polynomial calculated by both methods).
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Details
- Title
- Applications of Generalized Laplacian Matrices in Graph Tiling
- Creators
- Elizabeth Balmer
- Contributors
- Matthew Hudelson (Advisor)Judith McDonald (Committee Member)Michael Tsatsomeros (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 69
- Identifiers
- 99900581534301842
- Language
- English
- Resource Type
- Dissertation