Reddit reviews Modern Graph Theory (Graduate Texts in Mathematics)

A graph theory project! I just started today (it was assigned on Friday and this is when I selected my topic). I’m on spring break but next month I have to present a 15-20 minute lecture on graph automorphisms. I don’t necessarily have to, but I want to try and tie it in with some group theory since there is a mix of undergrads who the majority of them have seen some algebra before and probably bored PhD students/algebraists in my class, but I’m not sure where to start. Like, what would the binary operation be, composition of functions? What about the identity and inverse elements, what would those look like? In general, what would the elements of this group look like? What would the group isomorphism be? That means it’s a homomorphism with a bijective function. What would the homomorphism and bijective function look like? These are the questions I’m trying to get answers to.

Last semester I took a first course in Abstract Algebra and I’m currently taking a follow up course in Linear Algebra (I have the same professor for both algebra classes and my graph theory class). I’m curious if I can somehow also bring up some matrix representation theory stuff as that’s what we’re going over in my linear algebra class right now.

This is the textbook I’m using for my graph theory class: Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/1846289696?ref=yo_pop_ma_swf

Here are the other graph theory books I got from my library and am using as references: Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/3662536218?ref=yo_pop_ma_swf

Modern Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/0387984887?ref=yo_pop_ma_swf

And for funsies, here is my linear algebra text: Linear Algebra, 4th Edition https://www.amazon.com/dp/0130084514?ref=yo_pop_ma_swf

But that’s what I’m working on! :)

And I certainly wouldn’t mind some pointers or ideas or things to investigate for this project! Like I said, I just started today (about 45 minutes ago) and am just trying to get some basic questions answered. From my preliminary investigating in my textbook, it seems a good example to work with in regards to a graph automorphism would be the Peterson Graph.

Perhaps Bollobas' Modern Graph Theory?

I'd recommend doing mathematics, It's much important than learning a language. It helps you grab the logic of solving a problem.


Discrete Mathematics by Rosen is the best book from my experience.



Graph Theory by Bollobas is recommended by many but i prefer Graph Theory by Douglas West




Algorithms by Cormen. No introductions needed this book encompasses most of the problems you'll encounter.



However if you're keen on learning a C/C++/Java i'd recommend the Head First Series from O'Reily .




Goodluck!

Thank you! This is exactly what I was looking for!!!! I didn't think anyone was going to give me a sufficient reply because there are a lot of books (sorry), but this is what I wanted. Where would you place the two books I linked, Principles and Techniques in Combinatorics and Introduction to Combinatorial Mathematics, Liu, in that list or would you consider studying them a redundant exercise? I also did not include this book in the list, but where would you place Problems from the Book and its accompanying Straight from the Book?

I will likely end up replacing the Graph Theory book I have in the list, by Berge, with Modern Graph Theory by Bellobas, since Berge doesn't have exercises, but I will assume it stays in the same order of the sequence.


I apologize for not initially including them. I did not realize that I did not. Also, are there any other topics you would recommend I cover for establishing a solid foundation. I didn't buy Rudin's Complex Analysis because I didn't know if that kind of thing was necessary. I don't even know what other branches of mathematics Complex Analysis relates to. There could be other topics I'm not aware of as well. Please don't hesitate to make more recommendations. I appreciate it.

My suggestion would be to go to a library, walk down the aisle scanning each graph theory textbook for a few minutes and then choose one which clicks. Having access to exercises is super important (accompanying solutions is nice.)

Having access to a few textbooks is nice because if you get stuck on a concept in your 'main' text you can see if the others explain the idea better (wikipedia is also good for this.) Be alert for problems arising from differences in notation if you do this though.

Free online text book: http://diestel-graph-theory.com/basic.html

One I purchased: http://www.amazon.com/Modern-Graph-Theory-Bela-Bollobas/dp/0387984887

Combinatorics via exercises: http://www.amazon.com/Combinatorial-Problems-Exercises-Second-Lovász/dp/044481504X

Check a university library for copies of the latter two.


University courses:
http://www1.maths.leeds.ac.uk/~pmt6sbc/3032/3032.html
http://users.utu.fi/harju/graphtheory/graphtheory.pdf
http://www-math.ucdenver.edu/~wcherowi/courses/m4408/gtln.html
http://www.personal.psu.edu/cxg286/Math485.pdf
http://www.warwick.ac.uk/~masgax/notes.pdf
http://www.cs.elte.hu/~karolyi/GT/index.html
http://ocw.mit.edu/courses/mathematics/18-315-combinatorial-theory-introduction-to-graph-theory-extremal-and-enumerative-combinatorics-spring-2005/