= Solution
{c}
There are four topologies for the one-loop <gluon self-energy>, shown in the upper row of the figure:
* A closed <quark> loop with the two external <gluons> attached through quark-gluon <Feynman vertices>, summed over active <quark flavors>.
* A loop of two internal <gluons> joining two three-gluon <Feynman vertices>, each carrying one external <gluon>.
* A closed <Faddeev-Popov ghost field> loop with two ghost-gluon <Feynman vertices>.
* A single four-gluon <Feynman vertex> with two external <gluons> and its remaining two legs contracted into a <tadpole diagram>.
The two internal-<gluon> graphs have <symmetry factor> $1/2$. The directed <quark> and <ghost loops> have <symmetry factor> one and a minus sign for a closed anticommuting loop. The four-gluon <tadpole diagram> must be included in the list even though its massless <Feynman integral> vanishes in <dimensional regularization>. Local <counterterms> are excluded here.
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