Application of algebraic topology to graphs and networks Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/1r66j463v

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  • In this thesis some applications of algebraic topology are given. Kirchhoff's circuit laws are translated into the language of algebraic topology: If G is the graph of a network N, if i is a current distribution and if v is a voltage distribution of N, then the two Kirchhoff laws become: (1) A current distribution is any vector i such that is a 1-cycle of G. (2) A voltage distribution is any cochain vector v such that v is a coboundary of G. Furthermore Kuratowski's and MacLane's planar graph theorems are proven and finally the problem of network duality is solved: Two networks N and N are dual if and only if their respective graphs G and G are planar.
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  • File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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  • description.provenance : Made available in DSpace on 2013-09-25T20:58:44Z (GMT). No. of bitstreams: 1 GerlachSiegfried1979.pdf: 527140 bytes, checksum: e3b23edcfacce2f09e158ad12fb58f69 (MD5) Previous issue date: 1979-05-03
  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2013-09-18T15:35:51Z (GMT) No. of bitstreams: 1 GerlachSiegfried1979.pdf: 527140 bytes, checksum: e3b23edcfacce2f09e158ad12fb58f69 (MD5)
  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2013-09-25T20:58:44Z (GMT) No. of bitstreams: 1 GerlachSiegfried1979.pdf: 527140 bytes, checksum: e3b23edcfacce2f09e158ad12fb58f69 (MD5)
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