I suppose, I could create a theoretical upper limit to how many edges each vertex could have, and I could index each vertex by just enumerating them....
Specifically, for graph theory and combinatorics, most mathematicians who do active research in those areas are heavily involved in computer science...
Even worse, in measure theorhetic terms, we use f^2 to mean f·f, but once you claim we're using the Lebesgue measure and f is Riemann integrable, f^2...
Category theory and type theory open up problems that set theory works for. It doesn't solve things, it just moves problems from one area to another...