## Isomorph-free exhaustive generation algorithms for association schemes

- Isomorfvrije exhaustieve, Jan Degraer, Kris Coolsaet
- 2007

1 Excerpt

- Published 2000

(otherwise we divide the vector by an appropriate scalar), so w.l.o.g. we have uj = 1 for a certain j ∈ {1, . . . , v}. The absolute value |(A~u)j| of the j-th component of A~u is at most ∑ i∼j |ui|; since the absolute values of all components of ~u are less than or equal to 1, we have ∑ i∼j |ui| ≤ k. On the other hand |(A~u)j| must be equal to |ρuj| = |ρ|, from which we obtain |ρ| ≤ k. If ρ = k, then we have ∑ i∼j ui = kuj = k, so ui = 1 for all vertices i which are adjacent

@inproceedings{Haemers2000MatrixTF,
title={Matrix techniques for strongly regular graphs and related geometries},
author={W . Haemers},
year={2000}
}