the Hoffman bound above.

Now the Delsarte bound applies not only to strongly regular graphs, but also to the graphs $\{\Gamma_1,\ldots,\Gamma_d\}$ of the relations (other than equality) of any $d$-class symmetric association scheme (see [@GM16 Corollary 3.7.2]). Thus, if $\Gamma$ is such a graph, having valency $k$ and least eigenvalue $s$, then $\omega(\Gamma)\leqslant \lfloor 1-k/s\rfloor$.

Here is an interesting illustrative example. Let $\Delta$ be the edge graph (or line graph) of the incidence graph of the projective plane of order $2$. Then $\Delta$ is the unique distance-regular graph with intersection array $\{4,2,2;1,1,2\}$. Now let $\Delta_3$ be the graph on the vertices of $\Delta$, with two vertices joined by an edge if and only if they have distance $3$ in $\Delta$. Then $\Delta_3$ is the graph of a relation in the usual symmetric association scheme associated with a distance-regular graph, where two vertices are in relation $i$ precisely when they are at distance $i$ in the distance-regular graph. The graph $\Delta_3$ has diameter $2$ and is edge-regular (but not strongly regular) with parameters $(v,k,\lambda)=(21,8,3)$. The clique adjacency bound for $\Delta_3$ is $4$. The least eigenvalue of $\Delta_3$ is $-\sqrt{8}$, and the Delsarte bound gives $3$, and indeed, $\omega(\Delta_3)=3$. However, the complement 