  In parking problems, a given number of cars enter a one-way street
sequentially, and try to park according to a specified preferred spot in the
street. Various models are possible depending on the chosen rule for
collisions, when two cars have the same preferred spot. In classical parking
functions, if a car's preferred spot is already occupied by a previous car, it
drives forward and looks for the first unoccupied spot to park. In this work,
we introduce a variant of classical parking functions, called "friendship
parking functions", which imposes additional restrictions on where cars can
park. Namely, a car can only end up parking next to cars which are its friends
(friendship will correspond to adjacency in an underlying graph). We
characterise and enumerate such friendship parking functions according to their
outcome permutation, which describes the final configuration when all cars have
parked. We apply this to the case where the underlying friendship graph is the
cycle graph. Finally, we consider a subset of classical parking functions,
called "cyclic parking functions", where cars end up in an increasing cyclic
order. We enumerate these cyclic parking functions and exhibit a bijection to
permutation components.
