= Complete one-loop connected cubic three-point graphs
For a real <phi cubed theory> with labelled external points, the connected three-point function at third order in the <coupling constant (physics)> has seven labelled <one-loop Feynman diagrams>: one triangle, three external-branch bubble insertions, and three tadpole-ended chains. The <symmetry factors> are respectively $1,2,2$, with graph weight $1/S$. To prove completeness, use $3V=2I+3$ and $L=I-V+1$: $V=3$ gives $I=3$ and $L=1$. The unique internal cycle is then a triangle, a pair of parallel edges, or a self-loop; the degree-three condition fixes the external attachments. Only the triangle remains <one-particle irreducible> after <amputation of external propagators>. A tadpole-free prescription removes the three chains but must be stated separately.
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