A network is said to have Sense of Direction
when the port labeling satisfies a particular set of global
consistency constraints.
In this paper we study the link between the topology
of a system and the number of labels that are necessary to
have a Sense of Direction in that system.
We consider systems whose topology is a regular graph and we study
the relationship between structural properties of d-regular graphs
and existence of a Sense of Direction which uses exactly d labels
(minimal SD).
In particular, we identify a property (Cycle Symmetricity)
which we show is a necessary condition for minimal SD.
Among regular graphs, we then focus on Cayley Graphs and
we prove that they always have a minimal Sense of Direction.