The number of disk graphs

A disk graph is the intersection graph of disks in the plane, and a unit disk graph is the intersection graph of unit radius disks in the plane. We give upper and lower bounds on the number of labelled unit disk and disk graphs on n vertices. We show that the number of unit disk graphs on n vertices is n · α(n) and the number of disk graphs on n vertices is n · β(n), where α(n) and β(n) are Θ(1). We conjecture that there exist constants α, β such that the number of unit disk graphs is n · (α+ o(1)) and the number of disk graphs is n · (β + o(1)).