(Part 2) Best graph theory books according to redditors
We found 82 Reddit comments discussing the best graph theory books. We ranked the 31 resulting products by number of redditors who mentioned them. Here are the products ranked 21-40. You can also go back to the previous section.
Here's a nonstandard answer but I think it has merit: I would love to drop a modern textbook on graph theory into the hands of Euler and his contemporaries, not so much to share the results contained therein but to standardize some terminology, notation, and ways of thinking.
I read a fascinating book recently: Graph Theory 1736-1936 by Biggs, Lloyd, and Wilson. It covers some of the major advances in the field over its first 200 years and, most significantly, shares large portions of the original papers published by the giants of the field: Euler, Vandermonde, Hamilton, Cayley, Prufer, Kempe, Sylvester, Tait, Petersen, Kuratowski, Konig, .... that's just a selection, mind you. I read the whole book but found myself often frustrated with how everyone seemed to have their own terminology and notation for essentially the same objects. I believe that, had some standard been established much earlier, these great minds could have made even more advances than they did since they could have communicated with each other more freely and clearly and had more convenient ways of representing their ideas.
For example, any modern presentation of Euler's solution to the Konigsberg Bridge problem goes something like this: Represent the land masses as vertices and the bridges as edges. Notice that an Eulerian circuit exists if and only if every vertex has even degree because such a circuit has to leave a vertex after entering it. But look: the Konigsberg Bridge graph has all odd degree vertices. QED.
Of course, Euler's solution looks nothing like this. He takes a few pages to describe the problem and his formulation of a tour as a sequence of letters representing the land masses and bridges used. For example, he wrote this as an example of a tour: EaFbBcFdAeFfCgAhCiDkAmEnApBoElD. Gosh, I got frustrated just trying to copy that down right now. If Euler had the notions of vertices and edges and incidence and degree and ... all of these things that are so downright obvious to modern graph theorists ... well, just imagine what he could have accomplished.
I teach math in college. We have a bulletin board where we post math puzzles for students to solve, and the prize for the best solution is a Dover book of the student's choice (we keep a box of them for this purpose). I've had a former student, now an assistant professor, come to my office years later to tell me that winning "Ruler and the round" and "Fifty Challenging Problems in Probability", and reading those books cover to cover during summer, was instrumental in convincing her to pursue a graduate education in mathematics.
Neat - there's someone is interested in the same field as me. Here's some resources on the topic.
Dr. Fan Chung of UCSD is considered one of the premier experts in the field. She has plenty of resources on it on her website. Link to her website
Dr. Steve Butler from Iowa State (who studied under Dr. Chung) has a playlist of his course lectures on it. Each video has a link to the notes. Link to playlist
Another expert on the subject I've met is Dr. Paul Horn, another student of Dr. Chung. Link to his website
Books:
Godsil and Royle's book on Algebraic Graph Theory. This is a good intro to the combined study of algebra and graph theory and has a couple chapters all about graph matrices. I would consider it essential for someone just getting into the topic, especially as an upper-level undergraduate.
Svetkovic, Rowlinson, & Simic's "An Introduction to the Theory of Graph Spectra". I consider this to be a little light on depth in any topic but it gives you an exceptionally diverse taste of all the different types of problems in the field.
Dr. Chung's lecture notes on spectral graph theory. She compiled these notes from a series of talks she did on the subject in the 90's. The notes have more depth but less breadth than the previous book I listed. Also not to brag or anything, but I got my copy signed by her at last year's JMM.
I hope these resources will be useful to you. Happy hunting.
They have an application to the Rubik's Cube. God's Number is a result about the diameter of the Cayley graph of the Rubik's Cube. Dan's Bump and Aurbach analyze the Cayley graph of the 2x2 cube here
Large groups with whose Cayley Graphs are of small diameter are of interest in networks, see Bien's paper "Constructions of Telephone Networks by Group Representations" or Schellwat. An important class of these are known as expanders (see here for applications of expanders) and an important class expanders are the Ramunujan graphs. Examples of Ramanujan graphs have been constructed with Cayley graphs, for a nice exposition, see Ram Murty.
You probably won't see much past a definition of Cayley graphs in a standard algebra class. You won't see it in a graph theory class because group theory is not usually a pre-req for graph theory. You might see a hint of it in an algebraic graph theory class if your instructor has some background in group theory. Don't let this put you off the subject though, the material is pretty accessible. If you're interested I'd advise starting off with Krebs and Shaheen's Expander Families and Cayley Graphs: A Beginner's Guide. If you know what a group and a graph are, you'll be ready to dive in.
I'd highly recommend the following books:
https://www.amazon.com/Theory-Demand-Printing-Advanced-Program/dp/0201410338
https://www.amazon.com/Mathematical-Problems-Proofs-Combinatorics-Geometry-ebook/dp/B000TYXW0M/ref=sr_1_5?keywords=Mathematical+Problems+and+proofs&qid=1573147419&s=books&sr=1-5
If you're a computer scientist, these two books will put you on a solid path for solving any math problems you're confronted with.
And though an interview, and not a lecture, this FT interview with Mandelbrot on the Efficient Markets Hypothesis is great:
https://www.youtube.com/watch?v=vxbxXBrOPS8
If he doesn't already have it, I find Doug West's book on the subject to be quite useful. Doug is also pretty cool, so that's another reason to buy his book.
Combinatorics and elementary number theory are pretty accessible at your stage right now. There are also some books that deal with the basics of group theory that you could look into (I read this in high school and it's pretty great for an introduction).
Check out chapter 9 of this book by Givens and Hoeting.
I think someone doing graphs and combinatorics for the first time should check out Combinatorics and Graph Theory by Harris, Mossinghoff et. al. I found the book to fit my learning style very well and helped me get a 98 in my first C&O course.
Brief, well written explanations, good instructive exercises, and a lot of enrichment sections on interesting topics like Ramsey numbers in the graph theory section.
The third section also gives an introduction to infinite graph theory.
Its also very up to date and is thoroughly referenced which is nice if you want to learn more about a given topic.
http://www.amazon.com/Combinatorics-Graph-Theory-Undergraduate-Mathematics/dp/1441927239/ref=sr_1_1?ie=UTF8&s=books&qid=1293475064&sr=8-1
I have a pdf copy if someone can think of an easy way for me to share it.
If by configuration graphs you mean configuration model (take a sequence of degrees and search for a random graphs with this sequence of degrees) then the main results can be found here:
https://www.amazon.fr/Random-Graphs-B%C3%A9la-Bollob%C3%A1s/dp/0521797225
I also found this course which seems good to begin with:
http://tuvalu.santafe.edu/~aaronc/courses/5352/fall2013/csci5352_2013_L11.pdf