English

Construction of divisible design graphs using affine designs

Combinatorics 2025-02-19 v1

Abstract

A kk-regular graph on vv vertices is a {\em divisible design graph} if there exist integers λ1,λ2,m,n\lambda_1,\lambda_2,m,n such that the vertex set can be partitioned into mm classes of size nn and any two different vertices from the same class have λ1\lambda_1 common neighbours, and any two vertices from different classes have λ2\lambda_2 common neighbours. In this paper, a new construction that produces divisible design graphs is provided.

Keywords

Cite

@article{arxiv.2502.12503,
  title  = {Construction of divisible design graphs using affine designs},
  author = {Vladislav V. Kabanov},
  journal= {arXiv preprint arXiv:2502.12503},
  year   = {2025}
}

Comments

8 pages. arXiv admin note: text overlap with arXiv:2111.10799

R2 v1 2026-06-28T21:48:12.453Z