On distance-regular Cayley graphs of generalized dicyclic groups

Abstract

Let $G$ be a generalized dicyclic group with identity $1$. An inverse closed subset $S$ of $G\setminus \{1\}$ is called minimal if $⟨S⟩=G$ and there exists some $s\in S$ such that $⟨S\setminus \{s,s^{-1}\}⟩\ne G$. In this paper, we characterize distance-regular Cayley graphs $\mathrm{Cay}(G,S)$ of $G$ under the condition that $S$ is minimal.

12 pages