Vertex parity of a QED amplitude ($V=2I_{\gamma }+E_{\gamma }$)

Each elementary QED vertex has one photon leg, so counting these legs gives $V=2I_{\gamma }+E_{\gamma }$. An amplitude with two external photons has even $V$. In particular Compton scattering has no cubic-order elementary-vertex contribution. With four external legs and $V=4$, a connected diagram has four internal lines and one loop.