I need some suggestions from the researchers to study the research field(s) in graph theory other than chemical graph theory. I shall be thankful if someone guide me and also share some related study material.
I suggest that you visit the wb page of one of the leading figures in Graph Theory: Douglas B. west, you will find a lot of materials, open problems and so on.
Spectral graph theory is one of the emerging areas in graph theory, which has several applications. For details, you can go through the book on "Graphs and Matrices" by R.B. Bapat.
Mathematical Combinatorics, or mathematcics over graphs and complex network, etc. is the central source for creation by graphs,. More new notions can be found in the www.mathcombin.com/notions.
Graph theory interlink with Harmonic Analysis is also an interesting topic Like the paper Article Best constants for the Hardy-Littlewood maximal operator on ...
also the paper Article Geometric properties of infinite graphs and the Hardy-Little...