File:Dih 4 Cayley Graph; generators a, b; in permutohedron section.svg

One of the Cayley graphs of the dihedral group Dih₄

The red arrow represents permutation ${\displaystyle a={\mathit {13}}}$, and the blue edge represents permutation ${\displaystyle b={\mathit {7}}}$.

The red arrow from ${\displaystyle {\mathit {16}}}$ to ${\displaystyle {\mathit {21}}}$ means ${\displaystyle {\mathit {16}}\cdot a={\mathit {16}}\cdot {\mathit {13}}={\mathit {21}}}$.

The blue edge between ${\displaystyle {\mathit {2}}}$ and ${\displaystyle {\mathit {10}}}$ means that ${\displaystyle {\mathit {2}}\cdot b={\mathit {2}}\cdot {\mathit {7}}={\mathit {10}}}$ and ${\displaystyle {\mathit {10}}\cdot b={\mathit {10}}\cdot {\mathit {7}}={\mathit {2}}}$.

There is also: left action last ⋅ first

This is: right action first ⋅ last