= Solution
For <four-momentum> $k$ flowing along the <fermion flow>, the <momentum space> <Feynman rules> are
$$
\boxed{\begin{aligned}
\text{scalar line: }&\frac{i}{k^2-m^2+i0},\\
\text{fermion line of species }i\text{ to }j:\quad&\delta_{ij}\frac{i(\not k+m)}{k^2-m^2+i0},\\
\phi\bar\psi_i\psi_j\text{ vertex: }&-ig\delta_{ij}.
\end{aligned}}
$$
The <scalar propagator> and <Dirac propagator> invert their respective quadratic kernels. The <interaction vertex> follows by expanding $\exp(i\int\mathcal L_{\rm int})$, fixing its sign. Species is conserved along each open <fermion> line; there is no vertex changing species 1 into species 2.
An <interaction vertex> carries $(2\pi)^4\delta^{(4)}(\sum k)$ with inward <four-momenta>. Impose <momentum conservation> and integrate each independent <loop momentum> with $d^4k/(2\pi)^4$. Include the <closed fermion loop sign> $-1$ for every <fermion loop>, the relevant <fermionic signs> when rearranging external states, and the <Feynman-diagram symmetry factor>. External incoming and outgoing <fermions> carry $u_s(p)$ and $\bar u_s(p)$; incoming and outgoing <antifermions> carry $\bar v_s(p)$ and $v_s(p)$. An external <real scalar field> leg has factor 1 in an amputated <scattering amplitude>. The <Feynman i-epsilon prescription> specifies the poles.
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