Request for introductory book on graph theory

[tbrown122387]

I'm looking for the title to a popular introductory book on graph theory. For the best possible recommendation, perhaps it would be wise for me to give you signals of my academic maturity.

I completed undergraduate math major in May 2010. Since then I've been working, but I'm looking to get back into grad school. Currently I get textbook names from first year graduate level classes, work through them, and write up the solutions. I've been doing this for approximately one month, and have made it halfway through Principles of Mathematical Analysis (Rudin) and Abstract Algebra (Dummit, Foote). Probably a little less than halfway for the second one, actually.

I also anticipate answers of the form, "well make sure you've read books like this one first." According to Wikipedia, group theory and combinatorics are related areas; I've taken undergrad classes in the former but not the latter.

Thanks in advance for responses, and apologies in advance for inadequate use of the forum's search feature.

 

[chiro]

Hey there thrown122387 and welcome to the forums.

If you haven't had many encounters with group theory or combinatorics I recommend you start with a book on the field of "Discrete Mathematics".

Basically discrete mathematics consists of mathematics that do not involve limits of some kind or things related to this. Under the guise of "Discrete Mathematics" you get combinatorics, graph theory, probability, set theory and other topics.

One book that has been around for a while (and has had many revisions) is the book by Kenneth Rosen. Once you get a feel for the basics then you can find more specialized books that deal with particular aspects of a subject.

Right now I'm reading an ebook called "Combinatorics - Topics, Techniques and Algorithms" by P Cameron and it looks very dense in terms of content and scope.

 

[kdbnlin78]

Hi there.

I can recommend "lecture notes in Graph Theory" by Tero Harju.

I am certain that if you use a popular browser and search the title and author above you will be able to find a pdf of the entire book. That's how I have mine.

Best wishes
kdbnlin.

 

[tbrown122387]

Found them both. I love the internet. Thanks guys.

 

[blue_raver22]

Dear requestor,

Thank you for reaching out for a recommendation on an introductory book on graph theory. Based on your academic background and current pursuits, I would highly recommend "Introduction to Graph Theory" by Douglas B. West. This book is widely used in undergraduate and graduate level courses and provides a comprehensive introduction to the subject. It covers both basic and advanced topics in graph theory, making it suitable for readers at various levels of academic maturity.

In addition, I would also suggest "Graph Theory: An Introductory Course" by Adrian Bondy and U.S.R. Murty. This book is known for its clear explanations and examples, making it a great resource for self-study. It also includes exercises and solutions, which aligns with your current approach of working through textbooks and writing up solutions.

As you mentioned, group theory and combinatorics are closely related to graph theory. If you are interested in exploring these areas further, I would recommend "A First Course in Abstract Algebra" by John B. Fraleigh and "Combinatorics: Topics, Techniques, Algorithms" by Peter J. Cameron.

I hope these recommendations will be helpful in your pursuit of further knowledge in graph theory. Best of luck in your studies and future academic endeavors.

Sincerely,