On strongly regular graphs with μ ≥ 2

In this paper, we prove that any strongly regular graph with μ = 1 satisfies k ≥ (λ + 1)(λ + 2) and any strongly regular graph with μ = 2 is either a grid graph or satisfies k ≥ 1/2λ(λ + 3). This improves upon a previous result of Brouwer and Neumaier who gave a necessary restriction on the parameters of strongly regular graphs with μ = 2 and k < 1/2λ(λ + 3).