On Minimal Distance-Regular Cayley Graphs of Generalized Dihedral Groups

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 $S$.

The unit group of finite group algebra of a generalized dihedral group

Let [Formula: see text] be a generalized dihedral group of order 2n and 𝔽q be a finite field having q elements. In this note, we establish the structure of the unit group of [Formula: see text] for any odd n ≥ 3. This extends a result due to Kaur and Khan [Units in 𝔽2D2p, J. Algebra Appl. 13(2) (2014) 9pp., doi: 10.1142/S0219498813500904] as well as a result due to the authors [Units in 𝔽2kD2n, Int. J. Group Theory 3(3) (2014) 25–34].