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Polya's Enumeration Theorem: Number of colorings of n-gons and non isomorphic graphs,
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
2010 (English)Independent thesis Advanced level (degree of Master (One Year)), 15 credits / 22,5 HE creditsStudent thesis
Abstract [en]

Polya’s theorem can be used to enumerate objects under permutation groups. Using grouptheory, combinatorics and some examples, Polya’s theorem and Burnside’s lemma arederived. The examples used are a square, pentagon, hexagon and heptagon under theirrespective dihedral groups. Generalization using more permutations and applications tograph theory.Using Polya’s Enumeration theorem, Harary and Palmer [5] give a function whichgives the number of unlabeled graphs n vertices and m edges. We present their work andthe necessary background knowledge.

Place, publisher, year, edition, pages
2010. , p. 45
Keywords [en]
Generating function; Cycle index; Euler’s totient function; Unlabeled graph; Cycle structure; Non-isomorphic graph.
Identifiers
URN: urn:nbn:se:lnu:diva-6199OAI: oai:DiVA.org:lnu-6199DiVA, id: diva2:324594
Presentation
2010-06-14, B2034, Linnaeus University, 16:11 (English)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2010-06-16 Created: 2010-06-15 Last updated: 2010-06-16Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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