= Solution
Classify the connected contractions by the numbers $(r,4-r)$ of external slow legs on the two sextic vertices and by the number $c$ of fast propagators joining them. Besides the displayed $(2,2;c=4)$ graph, the distinct topologies are:
* $(2,2;c=2)$: two joining lines and one tadpole on each vertex.
* $(1,3;c=3)$: three joining lines and one tadpole on the one-external-leg vertex.
* $(0,4;c=2)$: two joining lines and two tadpoles on the vertex with no external legs.
* $(1,3;c=1)$: one joining line, two tadpoles on the one-external-leg vertex, and one tadpole on the three-external-leg vertex.
Exchanging the two vertices gives no new topology. All four are connected <Feynman diagrams> selected by the logarithm in the <cumulant expansion>. With an ideal sharp momentum shell and a projection at exactly zero external momentum, the single joining line in the last topology cannot carry shell momentum, so that topology gives zero to the local quartic coupling; it is still the remaining formal connected contraction.
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