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Is there any undergraduate textbook on graph theory using linear algebra? A request is a beginning with graph matrices that explain most concepts in graph theory?

P.s. This thread has more specific requests than this thread What are good books to learn graph theory?.

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dbm
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2 Answers2

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There is one such book I know about: Ravindra B. Bapat – Graphs and Matrices. I don't have a lot of experience with this book, but I think this should be accessible at the undergraduate level. It also contains a lot of references for further reading, so it seems like a good starting point.

Apart from that, most books on algebraic graph theory contain some linear algebraic methods, but those may shift their focus more towards other algebraic methods such as graph automorphisms and various graph polynomials.

Josse van Dobben de Bruyn
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  • Seems a nice book. But how about a real undergrad textbook on it? – dbm Nov 15 '15 at 19:17
  • Well, as I said, this is the only such book I know about. :-) Maybe someone else has a better suggestion. If I understand your reply correctly, you think this book is too advanced. Maybe you could be a little more specific about your expectations. For instance, you write that you want graph matrices to be used to explain most concepts in graph theory. Do you actually want to use graph matrices to explain, say, graph colouring, bipartite matching, planarity, connectivity, etcetera? Upon reading your question, I never thought this could actually be what you meant, but now I'm not so sure. :-) – Josse van Dobben de Bruyn Nov 16 '15 at 01:51
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    Yes, I wish to go explaining graph theory using graph matrices as far as possible including all the concepts you mentioned. – dbm Nov 16 '15 at 02:39
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    Ah, yes, I see. Then clearly my suggestion is not what you're looking for! I think you're going to have a hard time finding such a book, since most authors prefer to think about graphs in pictures instead of matrices. However, should such a book pop up, it would be very interesting indeed! :-) I never thought about approaching graph theory that way. – Josse van Dobben de Bruyn Nov 16 '15 at 04:34
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I collect some books below

  1. Graphs and Matrices by Bapat (as pointed out by Josse)

  2. Section 1.9 of Graph Theory: Springer Graduate Text GTM 173 By Reinhard Diestel covers linear algebra on graphs (2012, P.24)

  3. Section 4.6 of Graph Theory and Its Applications, Second Edition By Jonathan L. Gross, Jay Yellen (2005, p.197) covers, similarly.

  4. Handbook of Graph Theory (2014), 2nd Edition by Gross et all (massive book) where Chapter 6.4 and the Chapter 6 on Algebraic Graph Theory (picture about the book here and Algebraic Graph Theory overview here)

where my favourite books bolded are the book by Bapat and the Handbook, nice reference material with over 1k pages. The Graphs and Vector Spaces subsection is written by Krishnaiyan "KT" Thulasiraman.

Related questions

  1. First book on algebraic graph theory? (a bit broader perspective with things such as linear algebra, group theory, ...)

  2. What are good books to learn graph theory? (more elementary focus)

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hhh
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