Proper scalar-QED seagull-vertex diagrams ($V_C+2V_S=4$)

With zero quartic coupling, a proper one-loop vertex with two scalar and two labelled photon legs has two boxes, five triangles and two bubbles. A directed scalar chain connects the charged external ends; the internal photon joins its endpoints. Cubic vertices have one photon slot, seagulls two. All nine graphs have Feynman-diagram symmetry factor one with external labels fixed. At zero external momentum a transverse internal photon kills any graph with a cubic endpoint, leaving only the two seagull bubbles.