Graph Theory - what are related fields in maths? I am an undergraduate student who hoping to self teach Graph Theory. I have studied elementary graph theory before, and have recently started reading 'Bollobas - Modern Graph Theory'.
What are your recommendations after this? I have heard that topology and combinatorics are related to graph theory. What should I study alongside Graph Theory to gain deeper understanding of it?
I am not interested in applications to computer science by the way. And textbook recommendations are also welcomed.
Thank you.
 A: Regarding your request for textbook recommendations: check them out at Amazon or your local library 
Alon, N., The Probabilistic Method, John Wiley & Sons, 3rd Edition, 2008
Biggs, N., Algebraic Graph Theory, Cambridge University Press, 2nd Edition, 1996
Bondy, J. A., Graph Theory, Springer, 2008
Capobianco, M., Examples and Counterexamples in Graph Theory, Elsevier North-Holland, 1978
Diestel, R., Graph Theory, Springer, 4th Edition, 2012
Godsil, C., Algebraic Graph Theory, Springer, 2001
Graham, R. L., Concrete Mathematics, Addison-Wesley, 3nd Edition, 1994
Hartsfield, N., Pearls in Graph Theory, Dover, 2003
Jensen, T. R., Graph Coloring Problems, John Wiley \& Sons, 1995
Lovasz, L., Matching Theory, AMS, 2009
Lovasz, L., Combinatorial Problems and Exercises, AMS, 4nd Edition, 2007
A: Several things, including:


*

*Ramsey theory

*Algebraic Graph theory and its applications in group theory

*Spectral Graph theory and its applications in linear algebra

*Knot theory and topological graph theory and its applications in topology. 

A: I would recommend the book Graphs and Digraphs 5th edition by Zhang, Lesniak, and Chartrand.  It does a good job of covering many different aspects of graph theory: use of matrices (matrix-tree theorem, notably), topological graph theory (starts with the ubiquitous study of planar graphs and then moves to embedding graphs in surfaces of higher genus), Networks, and extremal graph theory and Ramsey theory (these are way at the end of the book as it takes a good deal of prior knowledge to study these things).  Largely, it does not go into things like enumerative graph theory or random graph theory, nor does it go into hyper graph theory or matroid theory.
