< 0$, $f(t) \in {\mathbb{Z}}$, and $g(t)$ is an integer at least $2$. We begin by stating one of the main results of this paper.

\[thm:CAB-Del\] Let $\Gamma$ be a strongly regular graph with parameters $(v,k,\lambda,\mu)$ and eigenvalues $k > r \geqslant s$. Then, $$C_\Gamma \left ( \left \lfloor -\mu/s \right \rfloor, \left \lfloor 2-k/s \right \rfloor \right ) < 0.$$

Follows from Corollary \[cor:meetDelsarte\] and Corollary \[cor:meetDelsarte1\] below.

Observe that, together with Theorem \[thm:CliqueAdjPol\], Theorem \[thm:CAB-Del\] shows that the clique adjacency bound always does as well as the Delsarte bound for strongly regular graphs.

Now we can state our first polynomial identity, which shows that the clique adjacency polynomial is negative at a certain point.

\[lem:CAP0\] Let $\Gamma$ be a connected strongly regular graph with parameters $(v,k,\lambda,\mu)$ and eigenvalues $k > r > s$. Then $$C_\Gamma(-\mu/s, 2-k/s) = {(2s-r)(r+1)} < 0.$$

The equality follows from direct calculation (see Appendix \[sec:comp\]), using the equalities in Proposition \[pro:SRG\]. The right-hand side is negative since $s < 0$ and $r \geqslant 0$.

Let $\Gamma$ be a strongly regular graph with parameters $(v,k,\lambda,\mu)$ such that both $\mu/s$ and $k/s$ are integers. Then by Lemma \[lem:CAP0\], together with Theorem \[thm:CliqueAdjPol\], we recover the Delsarte 