= Solution
Expanding the covariant derivative isolates the <ghost-gluon vertex> interaction
$$
\mathcal L_{\bar cAc}=-g f^{abc}(\partial^\mu\bar c^a)A_\mu^b c^c.
$$
The derivative acts on the antighost. With all momenta incoming, let its momentum be $k$, the gluon's Lorentz index be $\mu$, and their color indices be $(a,b,c)$ in the order $(\bar c,A,c)$. The convention $e^{-ikx}$ replaces $\partial^\mu$ by $-ik^\mu$, and multiplication by $i$ from $e^{iS}$ gives
$$
\boxed{V_{\bar c^aA_\mu^bc^c}=-g f^{abc}k_\mu.}
$$
Momentum conservation is implicit. The <structure constants> reflect the <Adjoint representation>, and the antighost momentum follows directly from its differentiated field. Reversing the momentum convention changes the displayed vertex sign consistently; exchanging the ghost and antighost source order also carries a <fermionic sign>.
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