Consider a calculation of photon vacuum polarization in scalar QED. The 1PI diagram which people calculate is this one,
But in scalar QED the seagull vertex is also possible
Then why not include a diagram like this one,
Which would then make the propagator sum to go something like this,
and so on.
Now my question is am I correct to add such a diagram? If not why? Also if indeed such terms are added in a full calculation please refer to articles which take these contributions into account.