Does graph theory have application in pure mathematics? I have read some part of graph theory,the  question pop up in my mind, does
it have application in pure mathematics?
I mean like number theory,analysis,algebra,toplogy .... etc
Can it be used to prove some problem in pure mathematics ?
Anyone have any idea ?
Graph Theory should be Pure Mathematics because we can study its elements in the way we would study any other geometric object in Geometry. Things get out of control when people call Inequalities Applied Mathematics or Analysis of Convex Functions Convex Analysis, but they do that... In my point of view, Inequalities and Convex Analysis are a horrendous  mistake. An inequality involving Real Analysis should be studied inside of Real Analysis: if we call that inequalities, then it is a branch of Analysis, not Applied Mathematics. If we study a real convex function, that could be inside of Real Analysis. In the same way, Graph Theory should be inside of Geometry if what we are doing there is dealing with geometric objects in the traditional way: studying the shape, producing reasoning that leads to calculations, and so on.
Graph Theory should be Pure Mathematics because we can study its elements in the way we would study any other geometric object in Geometry. Things get out of control when people call Inequalities Applied Mathematics or Analysis of Convex Functions Convex Analysis, but they do that... In my point of view, Inequalities and Convex Analysis are a horrendous  mistake. An inequality involving Real Analysis should be studied inside of Real Analysis: if we call that inequalities, then it is a branch of Analysis, not Applied Mathematics. If we study a real convex function, that could be inside of Real Analysis. In the same way, Graph Theory should be inside of Geometry if what we are doing there is dealing with geometric objects in the traditional way: studying the shape, producing reasoning that leads to calculations, and so on.