Perfect codes in quartic Cayley graphs of generalized dihedral groups

For a graph $\mathrm{\Gamma }=(V\mathrm{\Gamma },E\mathrm{\Gamma })$, a subset $D$ of $V\mathrm{\Gamma }$ is a perfect code in $\mathrm{\Gamma }$ if every vertex of $\mathrm{\Gamma }$ is dominated by exactly one vertex in $D$. In this paper, we classify all connected quartic Cayley graphs on generalized dihedral groups admitting a perfect code, and determine all perfect codes in such graphs.