Nonexistence of $srg(19,6,1,2)$: Combinatorial Proof

Abstract

An $srg(19,6,1,2)$ is the graph with the smallest parameter set in the family of strongly regular graphs with parameters $λ=1$ and $μ=2$ for which the respective graph doesn't exist. The proof of that fact is based on algebraic arguments, particularly, on the Integrality Test, the very usefull tool for studying strongly regular graphs. To our best knowledge, there have not been proofs of pure combinatorial nature. In this short paper, we have decided to fill in this gap.

Figures (2)

• Figure 1: The structure of $srg(19,6,1,2)$
• Figure 2: Illustration for the Theorem 1: left - for case 1, right - for case 2.

Theorems & Definitions (2)

• Theorem 1
• proof