- 2k + \lambda).$$ Then $\omega(\Gamma) \leqslant \lfloor -k/s \rfloor$.

Follows from Theorem \[thm:CliqueAdjPol\] together with Corollary \[cor:beatDel01\] below.

Currently Brouwer [@Brouwer:URL] lists the feasible parameter tuples for connected and co-connected strongly regular graphs on up to $1300$ vertices. Of these, about $1/8$ of the parameter tuples of type-II strongly regular graphs satisfy the hypothesis of Theorem \[thm:beatDelsarteNonConf\]. By the remark following Corollary \[cor:beatDel01\], it follows that Theorem \[thm:beatDelsarteNonConf\] can be applied to about $1/4$ of the complementary pairs of type-II strongly regular graphs on Brouwer’s list.

Note that the example in [@Soi:CAB15] of a strongly regular graph with parameter tuple $(144,39,6,12)$ is an example of a graph satisfying the hypothesis of Theorem \[thm:beatDelsarteNonConf\]; in fact, in this case, the conclusion of Theorem \[thm:beatDelsarteNonConf\] is satisfied with equality. The parameter tuple $(88,27,6,9)$ is the first parameter tuple in Brouwer’s list to which we can apply Theorem \[thm:beatDelsarteNonConf\] and whose corresponding graphs are not yet known to exist (or not exist).

Parameters of strongly regular graphs {#sec:parameters_of_strongly_regular_graphs}
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Here we state some well-known properties of strongly regular graphs and their parameters. The first two propositions are standard (see Brouwer and Haemers [@brou:spec11 Chapter 9] or Cameron and Van Lint [@CvL Chapter 