The theorem should probably say: There is exactly one arrow of color c_s pointing at g and there is exactly one arrow of color c_s pointing away from g. In particular, vertex that points at g is s^{-1}g while g points at sg. Wording of second sentence could be improved as it doesn't mention c_s.
The theorem should probably say: There is exactly one arrow of color c_s pointing at g and there is exactly one arrow of color c_s pointing away from g. In particular, vertex that points at g is s^{-1}g while g points at sg. Wording of second sentence could be improved as it doesn't mention c_s.