Construction of divisible design graphs using affine designs

2025/02/18 by Vladislav V. Kabanov, Kabanov, Vladislav V. · 1 citation
Business, Management and Accounting · Engineering · #Design Education and Practice #Manufacturing Process and Optimization #Product Development and Customization #math.CO

paper · pdf · doi:10.48550/arxiv.2502.12503

openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

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

Cited by

• Thin divisible designs graphs: an interplay between fixed-point free involutions of (v,k,λ)-graphs and symmetric weighing matrices

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