Zeta Functions of Finite Graphs
Ihara introduced the zeta function of a finite graph in 1966 in the context of <i>p</i>-adic matrix groups. The idea was generalized to all finite graphs in 1989 by Hashimoto. We will introduce the zeta function from both perspectives and show the equivalence of both forms. We will discu...
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2005
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ndltd-LSU-oai-etd.lsu.edu-etd-07072005-1210132013-01-07T22:49:55Z Zeta Functions of Finite Graphs Czarneski, Debra Mathematics Ihara introduced the zeta function of a finite graph in 1966 in the context of <i>p</i>-adic matrix groups. The idea was generalized to all finite graphs in 1989 by Hashimoto. We will introduce the zeta function from both perspectives and show the equivalence of both forms. We will discuss several properties of finite graphs that are determined by the zeta function and show by counterexample several properties of finite graphs that are not determined by the zeta function. We will also discuss the relationship between the zeta function of a finite graph and the spectrum of a finite graph. Bogdan Oporowski Lynn LaMotte Robert Perlis Stephen Shipman Lawrence Smolinsky Helena Verrill LSU 2005-07-07 text application/pdf http://etd.lsu.edu/docs/available/etd-07072005-121013/ http://etd.lsu.edu/docs/available/etd-07072005-121013/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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NDLTD |
| language |
en |
| format |
Others
|
| sources |
NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics Czarneski, Debra Zeta Functions of Finite Graphs |
| description |
Ihara introduced the zeta function of a finite graph in 1966 in the context of <i>p</i>-adic matrix groups. The idea was generalized to all finite graphs in 1989 by Hashimoto. We will introduce the zeta function from both perspectives and show the equivalence of both forms. We will discuss several properties of finite graphs that are determined by the zeta function and show by counterexample several properties of finite graphs that are not determined by the zeta function. We will also discuss the relationship between the zeta function of a finite graph and the spectrum of a finite graph. |
| author2 |
Bogdan Oporowski |
| author_facet |
Bogdan Oporowski Czarneski, Debra |
| author |
Czarneski, Debra |
| author_sort |
Czarneski, Debra |
| title |
Zeta Functions of Finite Graphs |
| title_short |
Zeta Functions of Finite Graphs |
| title_full |
Zeta Functions of Finite Graphs |
| title_fullStr |
Zeta Functions of Finite Graphs |
| title_full_unstemmed |
Zeta Functions of Finite Graphs |
| title_sort |
zeta functions of finite graphs |
| publisher |
LSU |
| publishDate |
2005 |
| url |
http://etd.lsu.edu/docs/available/etd-07072005-121013/ |
| work_keys_str_mv |
AT czarneskidebra zetafunctionsoffinitegraphs |
| _version_ |
1716476992127238144 |