Application of algebraic topology to graphs and networks

Graduate Thesis Or Dissertation

Public Deposited

Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/1r66j463v

Descriptions

Attribute Name	Values
Creator	Gerlach, Siegfried
Abstract	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.
Resource Type	Masters Thesis
Date Available	2013-09-25T20:58:44+00:00
Date Issued	1979-05-03
Degree Level	Master's
Degree Name	Master of Science (M.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	1979
Advisor	Kas, Arnold
Academic Affiliation	Mathematics
Non-Academic Affiliation	Oregon State University. Graduate School
Subject	Algebraic topology
Rights Statement	Copyright Not Evaluated
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]
Digitization Specifications	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.
Replaces	http://hdl.handle.net/1957/42847

Parents:

This work has no parents.

In Collection:

Thumbnail	Title	Date Uploaded	Visibility	Actions
	GerlachSiegfried1979.pdf	2017-08-23	Public	Download