Divisible design graphs obtained by plugging a difference set into a construction for antipodal distance-regular graphs of diameter 3

Bart De Bruyn; Sergey Goryainov; Ruilin Ma; Ruihan Xie

Divisible design graphs obtained by plugging a difference set into a construction for antipodal distance-regular graphs of diameter 3

Combinatorics 2026-07-06 v1

Authors: Bart De Bruyn , Sergey Goryainov , Ruilin Ma , Ruihan Xie

Abstract

In this paper, we present a new construction of divisible design graphs with new parameters, obtained by plugging a difference set of a quotient group into a known construction of antipodal distance-regular graphs of diameter 3. Also, we show that in characteristic 2 the new divisible design graphs are Cayley graphs over an elementary abelian 2-group.

Keywords

divisible design graphs difference sets antipodal distance-regular graphs Cayley graphs

Cite

@article{arxiv.2607.05043,
  title  = {Divisible design graphs obtained by plugging a difference set into a construction for antipodal distance-regular graphs of diameter 3},
  author = {Bart De Bruyn and Sergey Goryainov and Ruilin Ma and Ruihan Xie},
  journal= {arXiv preprint arXiv:2607.05043},
  year   = {2026}
}