Consider that I'm given the following Lagrangean:
where $\phi$ and $\chi$ are neutral scalar fields and $\psi$ is the electron field. From this Lagrangean I extract new Feynman rules besides QED's, for instance, the propagator for the scalar fields, the vertices of electrons and $\chi$ field, vertices between the scalar fields, etc.
Within QED, in particular, the one-loop correction to the vertex is done by introducing a photon propagator "connecting" the fermionic lines. Furthermore, the one-loop correction for the electron propagator introduces the electron's self energy and for the photon propagator, the vacuum polarization.
My question is, why are these the one-loop 1PI corrections to QED? How do I know that for the vertex, I need to connect those two electron lines with a photon? The reason I ask this is because I'm trying to draw the one-loop corrections for the scalar self energy $\chi$ and for the new vertices (so I can discuss their superficial degree of divergence after).