2023/11/14 by Xueyi Huang, Lu Lu, Huang, Xueyi +3
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.2311.08128
Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavič and Potočnik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural extension of the problem of characterizing strongly-regular Cayley graphs (or equivalently, regular partial difference sets). In this paper, we provide a partial characterization for distance-regular Cayley graphs over semi-dihedral groups and pseudo-semi-dihedral groups, both of which are 2-groups with a cyclic subgroup of index 2.