On Minimal Distance-Regular Cayley Graphs of Generalized Dihedral Groups

Abstract

Let $G$ denote a finite generalized dihedral group with identity $1$ and let $S$ denote an inverse-closed subset of $G \setminus \{1\}$, which generates $G$ and for which there exists $s \in S$, such that $\langle S \setminus \{s,s^{-1}\} \rangle \ne G$. In this paper we obtain the complete classification of distance-regular Cayley graphs $\mathrm{Cay}(G;S)$ for such pairs of $G$ and $S$.