Dissertation
Alpha Adjacency: A Generalization of Adjacency Matrices
Doctor of Philosophy (PhD), Washington State University
01/2020
Handle:
https://hdl.handle.net/2376/112391
Abstract
B. Shader and W. So introduced the idea of the skew adjacency matrix. Their idea was to give an orientation $\\ori$ to a simple undirected graph $G$ from which a skew adjacency matrix $S(G^\\ori)$ is created. The $\\alpha$-adjacency matrix extends this idea to an arbitrary field $\\mathbb{F}$.
To study the underlying undirected graph, the average $\\alpha$-characteristic polynomial can be created by averaging the characteristic polynomials over all the possible orientations. In particular, a Harary-Sachs theorem for the average $\\alpha$-characteristic polynomial is derived and used to determine a few features of the graph from the average $\\alpha$-characteristic polynomial. Also the number of graph which are cospectral under the average $\\alpha$-characteristic polynomial is determined for graphs on 9 or less vertices.
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Details
- Title
- Alpha Adjacency: A Generalization of Adjacency Matrices
- Creators
- Enzo Peter Wendler
- Contributors
- Judith McDonald (Advisor)Matthew Hudelson (Advisor)Sheng-Chi Liu (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
- 76
- Identifiers
- 99900581499501842
- Language
- English
- Resource Type
- Dissertation