Transformation laws for generalized Dedekind sums associated to Fuchsian groups

We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples are provided in the cases of the Hecke triangle groups, the Hecke congruence groups ${\mathrm{\Gamma }}_0(N)$, and the non-congruence arithmetic groups ${\mathrm{\Gamma }}_0(N{)}^{+}$.