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Math 314H Project : Applications of Linear Algebra to Graph Theory
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Due Date: Wednesday, April 25.
 
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Guidelines:
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 This project is a group project which is based on material found in the
 the textbook and other sources.
 Any other sources used must receive attribution in the report and be listed
 in its bibliography.
 Any outside help (other than the instructor) should likewise be acknowledged.
 The project is to be carried out with teams of one or two individuals.
 If you prefer to work alone on the project or choose your own partner,
 this is fine.
 Otherwise, I will assign partners for the project.
 It is expected that each partner will make a significant contribution to
 the project; this is a prerequisite for receiving full credit.
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The project will consist of two parts: a written report and a Maple notebook.
 The report you turn in should be a mix of equations, formulas, graphics
 and prose.
 Use complete sentences, good grammar, correct spelling and correct punctuation.
 You should write your project in such a way that it can be read and understood
 by anyone who knows the material for this course; do 
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not
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 write to the instructor.
 Finally, neatness counts, so the project should be neatly typed with hardcopy
 of the Maple notebook that you use.
 If you want a page count guideline, the written project by a single student
 should be at minimum three pages, and for a team of two, a minimum of five
 pages.
 (Just including the necessary background definitions, etc., will get you
 close to the minimum, so these numbers should be no problem.) There is no
 upper bound, but you are cautioned against turning in endless tables of
 numbers or listings.
 A high quality short report is 
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much
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 better than a mediocre long report.
 See page 43 of the text for some advice on project writing.
 
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The report will involve some calculations in your Maple notebook, but these
 need not be at the level of writing programs.
 You will find some helpful information in the notebook LinAlgMaple5.ms which
 you download by clicking on the Maple URL in the resources section of our
 home page.
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You can consult with me at any stage of your project for help or suggestions.
 I won't pre-grade your project, but I will look at your work and try to
 give you guidance.
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Description:
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 The purpose of this project is to explore applications of linear algebra
 concepts to graph theory, and to report on your findings.
 Your primary source is the textbook, which has numerous applications of
 linear algebra concepts to graph theory (see, e.g., pages 8, 66-69, 122-123,
 178-181, 210-212 and 303.) Some other references are given below; also feel
 free to consult any other references that you find.
 The goal of your report is to find and explain applications of as many
 linear algebra/matrix theory concepts as possible, and illustrate such
 applications with example(s) and calculations.
 Nearly every chapter of the text has some application to graph theory with
 the exception of Chapter 5 (the eigenvalue problem.) It would be very nice
 if you could track down a graph-theoretic application of this subject as
 well.
 
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\bibitem {1}

Algebraic Graph Theory, Norman Biggs, Cambridge University Press, 1974.
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\bibitem {2}

Introduction to Graph Theory, Douglas West, Prentice-Hall, Upper Saddle
 River (1966).
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\bibitem {3}

Introduction to Graph Theory, 2nd ed., Robin Wilson, Longman Group Ltd (1979).
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