My knowledge in topological graph theory is in low, I need some good reference which has two simple thing, Definition of new concepts (like genus,graph embedding in surface, ...) also contains related theorem on this topic, It's not essential to prove theorem, I think there should be something like wiki or good survey.

I found some books, but first of all I need some overview on it, maybe it's not necessary to have book to come up with my problems, I found something in wolfram but it's not integrated, and It's not easy to find all related things (because I don't know them) and print them all to have in hand. So first I need good bible (specially free).

In fact I'm working in some aspects of planar graphs and some other types of graph which are near to them (like graphs with small genus), everyone know about filed has any suggestion (book, book chapter, Advise, ... ) I'll be happy to know it.

Also If you know any theorem or definition, I'll be happy to know it, and sure upvote it, because if there isn't good reference is good create one here.

  • $\begingroup$ It seems to me that what you need is a very elementary introduction to the topology of surfaces. I don't have any suggestions, though. $\endgroup$ Mar 13, 2011 at 16:01
  • $\begingroup$ I didn't mean to insult you; I meant that out of all the introductions to the topology of surfaces, you should pick the most elementary. If there's a topology of surfaces introduction for non-mathematicians (e.g., physicists if not computer scientists), it'd be ideal. Apologies if I've offended you. $\endgroup$ Mar 14, 2011 at 12:48
  • $\begingroup$ @Peter, Thanks for your advise, that was my misunderstanding. $\endgroup$
    – Saeed
    Mar 14, 2011 at 12:55

3 Answers 3


My lecture notes on computational topology include some basic material on topological graph theory. They don't come anywhere close to the completeness of Archeacon's survey (or Giblin's book, Mohar and Thomassen's book, or Gross and Tucker's book), but you may still find them useful. (Start with "Curves on Surfaces".)

If you're a student, you may also find your local university library useful. Most mathematics libraries have copies of all the books I mentioned, and they will actually let you borrow them for free, possibly for several months at a stretch. Sadly, these books may only be available in a legacy format that is difficult to search and copy from, but hey, you get what you pay for.


For free introductions, I would search for lecture notes on the subject. For example, the results of this search might help you.

You may also be interested in the following paper:

This web page has links to two surveys on this topic, one of which is less technical and the other is more technical.

Edit 1: @Saeed: Orientable surfaces are defined in the "more technical" paper linked above. It is also defined in http://en.wikipedia.org/wiki/Orientability.


Archdeacon's survey Topological Graph Theory was almost mentioned already:



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