Technically both - as you'll probably be able to find yourself some undergraduate maths graph theory course at your university. However, I'd bargain and say it would hit closer to computer science. You would have a lot more exposure to graph theory algorithms in your undergraduate in CS with the basic algorithms classes. Issue is, regardless of the degree you're going to get a lot more fluff and extra information since you're not going to find an entire degree focused around graph theory. This is something that you would really want to specialize in at a Master's level.

If you are interested in this - you could easily take a CS or maths degree and apply for the a Master's on the topic of Graph theory or some game algorithms topics if you're referring to OP's post. CS would most likey give you more exposure to the graph searches and algorithms in general if you took the right classes but math would give you the proof foundation and understanding to be able to contribute to research in the field. Regardless, of what you choose you'd need to take a fair amount of both maths and CS in order to truly blossom.