<p>For <strong>free</strong> introductions, I would search for lecture notes on the subject. For example, the results of <a href="http://www.google.com/search?q=%22topological+graph+theory%22+site%3aedu">this search</a> might help you.</p>

<p>You may also be interested in the following paper:</p>

<ul>
<li><a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.1728">Topological Graph Theory - A Survey</a> by Cong. Num.</li>
</ul>

<p>This <a href="http://www.cems.uvm.edu/~archdeac/papers/papers.html">web page</a> has links to two surveys on this topic, <a href="http://www.cems.uvm.edu/~archdeac/papers/topgraph.ps">one of which</a> is less technical and <a href="http://www.cems.uvm.edu/~archdeac/papers/survey.ps">the other</a> is more technical.</p>

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

CC BY-SA 2.5
2011-03-13T13:30:09.380Z
2011-03-13T13:37:15.100Z
2011-03-13T13:37:15.100Z
Sadeq Dousti
<p>Archdeacon's survey <em>Topological Graph Theory</em> was almost mentioned already: </p>

<p><a href="http://www.math.u-szeged.hu/~hajnal/courses/PhD_Specialis/Archdeacon.pdf" rel="nofollow noreferrer">http://www.math.u-szeged.hu/~hajnal/courses/PhD_Specialis/Archdeacon.pdf</a></p>

CC BY-SA 3.0
2017-10-27T02:42:54.060Z
2017-10-27T02:42:54.060Z
Bjørn Kjos-Hanssen
<p><a href="http://compgeom.cs.uiuc.edu/~jeffe/teaching/comptop/schedule.html" rel="noreferrer">My lecture notes on computational topology</a> 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".)</p>

<p>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.</p>

CC BY-SA 2.5
2011-03-14T03:14:44.160Z
2011-03-14T03:14:44.160Z
Jeffε
<p>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.</p>

<p>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 <a href="http://mathworld.wolfram.com/" rel="noreferrer">wolfram</a> 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).</p>

<p>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.</p>

<p>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.</p>

CC BY-SA 2.5
2011-03-13T16:01:17.080Z
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.
Peter Shor 
CC BY-SA 2.5
2011-03-14T12:48:43.317Z
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.
Peter Shor 
CC BY-SA 2.5
2011-03-14T12:55:37.863Z
@Peter, Thanks for your advise, that was my misunderstanding.
Saeed
<reference-request><graph-theory><co.combinatorics><survey><topological-graph-theory>
Is there any good and free Introduction to topological graph theory
Saeed
# Is there any good and free Introduction to topological graph theory

(Asked by: username_0 on 2011-03-13)

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](http://mathworld.wolfram.com/) 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.

**Tags:** reference-request, graph-theory, co.combinatorics, survey, topological-graph-theory

> **Comments:**
> **username_1**: 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.  
> **username_1**: 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.  
> **username_0**: @Peter, Thanks for your advise, that was my misunderstanding.  

---

## 3 answers

### Answer by username_4 on 2011-03-14. Score: 10 | Accepted answer

[My lecture notes on computational topology](http://compgeom.cs.uiuc.edu/~jeffe/teaching/comptop/schedule.html) 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.


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### Answer by username_2 on 2011-03-13. Score: 5

For **free** introductions, I would search for lecture notes on the subject. For example, the results of [this search](http://www.google.com/search?q=%22topological+graph+theory%22+site%3aedu) might help you.

You may also be interested in the following paper:

* [Topological Graph Theory - A Survey](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.1728) by Cong. Num.

This [web page](http://www.cems.uvm.edu/~archdeac/papers/papers.html) has links to two surveys on this topic, [one of which](http://www.cems.uvm.edu/~archdeac/papers/topgraph.ps) is less technical and [the other](http://www.cems.uvm.edu/~archdeac/papers/survey.ps) is more technical.

**Edit 1:** @username_0: Orientable surfaces are defined in the "more technical" paper linked above. It is also defined in <http://en.wikipedia.org/wiki/Orientability>.


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### Answer by username_3 on 2017-10-27. Score: 1

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

<http://www.math.u-szeged.hu/~hajnal/courses/PhD_Specialis/Archdeacon.pdf>


---

