English

New versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs

Combinatorics 2021-12-01 v3

Abstract

A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1 ,lambda_2, m, n) if its vertex set can be partitioned into m classes of size n, such that any two different vertices from the same class have lambda_1 common neighbours, and any two vertices from different classes have lambda_2 common neighbours whenever it is not complete or edgeless. If m=1, then a divisible design graph is strongly regular with parameters (v, k, lambda_1, lambda_1). In this paper the Wallis-Fon-Der-Flaass construction of strongly regular graphs is modified to create new constructions of divisible design graphs. In some cases, these constructions lead to strongly regular graphs.

Keywords

Cite

@article{arxiv.2111.10799,
  title  = {New versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs},
  author = {Vladislav V. Kabanov},
  journal= {arXiv preprint arXiv:2111.10799},
  year   = {2021}
}

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13 pages