It's a classic result that a graph parameter called Lovasz theta-function $\theta(\Gamma)$ of a strongly regular graph $\Gamma$ is determined by its parameters. And the significance of $\theta(\Gamma)$ is that it is "sandwiched" between the clique number and the chromatic number.
In more detail, the parameters of the s.r.g. $\Gamma$ determine a 3-dimensional commutative algebra of symmetric matrices (the adjacency matrix $A(\Gamma)$ of $\Gamma$, the adjacency matrix of its complement, and the identity matrix span this algebra). Anything that can be expressed in terms of this algebra, which is specified by the eigenvalues of $A(\Gamma)$, is a parameter you are asking about, and $\theta(\Gamma)$ is one of them. Another one is the number of spanning trees, as by Matrix Tree Theorem it is determined by the eigenvalues.