A unit disk graph is the intersection graph
of a family of unit disks in the plane.
If the disks do not overlap, it is also a unit coin graph or penny graph.
It is known that finding a maximum independent set
in a unit disk graph is a NP-hard problem.
In this work we extend this result to penny graphs.
Furthermore, we prove that finding a minimum clique partition
in a penny graph is also NP-hard, and present
two linear-time approximation algorithms for the computation of clique partitions:
a 3-approximation algorithm for unit disk graphs
and a 2-approximation algorithm for penny graphs.