See
http://mathoverflow.net/questions/75030/clique-sizes-in-a-unit-disk-graph
and references mentioned there... Your graphs are the unit disk graphs of the title.
EDIT
See http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.7.4866&rep=rep1&type=pdf, especially the reference to Gupta/Kumar at the very beginning...

