Given a group action of on ,
there is a natural group action of on .
The orbits of this induced action are called orbitals or 2-orbits, group
a generalization being [[n-orbit|-orbits]].
The number of orbitals is called the rank.
If is an orbital, then so is its paired orbital
and if we say is self-paired.
An orbital admits a natural interpretation as a digraph, known as the orbital digraph,
where by abuse of notation we write and .
Properties
Suppose is an orbital, and identify it with the corresponding orbital digraph.