Some Open Mathematical Problems on Fullerenes.

Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as planar, 3-regular graphs with facets composed only of pentagons and hexagons. In this work, we outline a few of the many open questions about fullerenes, beginning with the problem of generating fullerenes randomly.