Cayley graph of D8

G = { a,b | a3=b2=1, ab=ba3 }
Set of elements / vertices {1, a, a2, a3, b, ba, ba2, ba3}
Generating set / colors {a, b} ( a yellow, b blue )
Two elements (x, y) are connected by an arc if y=ax (yellow arc), y=bx (blue arc).
Now you know the Cayley Graphs of all Dihedral Groups...