Bowen--Franks groups and minus class groups of imaginary abelian fields

$\mathrm{L}\mathrm{e}\mathrm{i}$, $\mathrm{M}\ddot{\mathrm{u}}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{r}$, and $\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{i}\grave{\mathrm{e}}\mathrm{r}\mathrm{e}\mathrm{s}$ constructed a directed graph for which the torsion part of the corresponding Bowen–Franks group is related to the minus part of the class group of a cyclotomic number field with prime conductor. We extend this result to a general imaginary abelian field.