bound, i.e., $\omega(\Gamma) \leqslant \left \lfloor 1-k/s \right \rfloor$. It remains for us to deal with the situation when $k/s$ and $\mu/s$ are not integers. In the remainder of this section, motivated by Lemma \[lem:CAP0\], we consider integral points $(x,y) \in {\mathbb{Z}}^2$ close to $(-\mu/s, 2-k/s)$ such that $C_\Gamma(x,y)$ is negative. We deal with the type I and type II cases separately.

Type-I strongly regular graphs {#sub:conference_graphs}
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Let $\Gamma$ be a type-I strongly regular graph (or conference graph) with $v$ vertices. By Proposition \[pro:SRGtI\] we have $-\mu/s = r$ and $-k/s = 2r$. Therefore, we consider integral points $(x,y)$ close to $(r,2+2r)$ at which to evaluate the clique adjacency polynomial. In view of Proposition \[pro:fracPart\], we evaluate $C_\Gamma(x,y)$ at points of the form $(r-t,a+2r-2t)$ for some $a \in \mathbb N$, thinking of $t$ as the fractional part of $r$.

\[lem:CAP2.0\] Let $\Gamma$ be a type-I strongly regular graph with $v$ vertices and eigenvalues $k > r > s$. Then $$\begin{aligned}
        C_\Gamma(r - t, 3 + 2r - 2t) &= 2(t-1)(t+s-2)(t+2s); \label{eqn:confPol3} \\
        C_\Gamma(r - t, 2 + 2r - 2t) &= (t+s)(2t^2+(4s-1)t-3s-1). \label{eqn:confPol2}
    \end{aligned}$$

The equalities follow from direct calculation (see Appendix \[sec:comp\]), applying Proposition \[pro:SRG\] and the definition 