Brouwer's 2-connectivity conjecture for strongly regular graphs

Let $G$ be a connected $(v,k,\lambda,\mu)$-strongly regular graph, and let $S$ be a disconnecting set of $G$ whose removal disconnects $G$ into non-singleton components. Brouwer's conjecture. One has

$$|S|\geq 2k-\lambda-2.$$

The bound $2k-\lambda-2$ is the size of the neighborhood of an edge and is therefore the natural candidate for the minimum such disconnecting-set size, denoted by $\kappa_2(G)$. The paper identifies this as Brouwer's 1996 conjecture; its general status is not resolved in the supplied text.