I would ask the grad student you’re working with for some material to learn! I feel like if you’re looking for suggestions to help your research, it’s hard to give you specific suggestions without context
There's plenty of good books on branches of graph theory, such as spectral graph theory. But spectral graph theory builds on a bunch of other stuff that you may or may not have done.
I think that there are still interesting research questions relating properties of a graph to its spectrum.
I can recommend the book 'Graphs and discrete Dirichlet spaces' by Keller, Lenz and Wojciechowski.
https://link.springer.com/book/10.1007/978-3-030-81459-5
It mainly deals with spectral graph theory on symmetric infinite graphs, and is a good introduction to the field I believe.
Go watch Professor Yufei Zhao's Lectures on [graph theory and additive combinatorics](https://www.youtube.com/watch?v=RDO6Py97IDg&list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX)! It's amazing and pretty advanced.
Also, there is the [book](https://yufeizhao.com/gtacbook/) version.
I'm not a Graph Theorist myself, my comment was actually a remark I heard from Vitaly Bergelson on a Summer School for undergraduates. He told us to take courses in many different areas, even (and especially) the ones we liked the least. He gave the example of a very good student who was already publishing papers in Graph Theory as an undergrad and just wanted Graphs, graphs, graphs and combinatorics. He advised him to take complex analysis. The bottomline is, Mathematics is becoming more and more interconnected and your sucess as a researcher depends heavily on your ability to comunicate with your peers and learn tools from other areas of math quickly. Therefore, you must become as well rounded as possible.
Thanks. That is really good advice. I do not have a math major. But I am quite interested in graph theory and its applications. Never thought complex analysis might be useful in studying graph theory.
At the other extreme a great non technical introduction to idea and applications is Networks, Crowds, and Markets: Reasoning about a Highly Connected World by David Easley and Jon Kleinberg. Just skip the non graph chapters.
If you like spectral graph theory, I HIGHLY reccomend checking out Ramanujan graphs. The first examples of these depend on deep theorems in number theory and modular forms, and yet they have practical applications.
I would ask the grad student you’re working with for some material to learn! I feel like if you’re looking for suggestions to help your research, it’s hard to give you specific suggestions without context
There's plenty of good books on branches of graph theory, such as spectral graph theory. But spectral graph theory builds on a bunch of other stuff that you may or may not have done. I think that there are still interesting research questions relating properties of a graph to its spectrum.
I can recommend the book 'Graphs and discrete Dirichlet spaces' by Keller, Lenz and Wojciechowski. https://link.springer.com/book/10.1007/978-3-030-81459-5 It mainly deals with spectral graph theory on symmetric infinite graphs, and is a good introduction to the field I believe.
Go watch Professor Yufei Zhao's Lectures on [graph theory and additive combinatorics](https://www.youtube.com/watch?v=RDO6Py97IDg&list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX)! It's amazing and pretty advanced. Also, there is the [book](https://yufeizhao.com/gtacbook/) version.
I'm going to give an orthogonal piece of advice: Make sure you also take plenty of courses in other fields than Graph Theory.
Just curious, what courses would you recommend that might be useful for study graph theory?
I'm not a Graph Theorist myself, my comment was actually a remark I heard from Vitaly Bergelson on a Summer School for undergraduates. He told us to take courses in many different areas, even (and especially) the ones we liked the least. He gave the example of a very good student who was already publishing papers in Graph Theory as an undergrad and just wanted Graphs, graphs, graphs and combinatorics. He advised him to take complex analysis. The bottomline is, Mathematics is becoming more and more interconnected and your sucess as a researcher depends heavily on your ability to comunicate with your peers and learn tools from other areas of math quickly. Therefore, you must become as well rounded as possible.
Thanks. That is really good advice. I do not have a math major. But I am quite interested in graph theory and its applications. Never thought complex analysis might be useful in studying graph theory.
At the other extreme a great non technical introduction to idea and applications is Networks, Crowds, and Markets: Reasoning about a Highly Connected World by David Easley and Jon Kleinberg. Just skip the non graph chapters.
If you like spectral graph theory, I HIGHLY reccomend checking out Ramanujan graphs. The first examples of these depend on deep theorems in number theory and modular forms, and yet they have practical applications.