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We use semidefinite programming to bound the fractional cut-cover parameterof graphs in association schemes in terms of their smallest eigenvalue. We alsoextend the equality cases of a primal-dual inequality involving theGoemans-Williamson semidefinite program, which approximates \textsc{maxcut}, tographs in certain coherent configurations. Moreover, we obtain spectral boundsfor \textsc{max 2-sat} when the underlying graphs belong to a symmetricassociation scheme by means of a certain semidefinite program used toapproximate quadratic programs, and we further develop this technique in orderto explicitly compute the optimum value of its gauge dual in the case ofdistance-regular graphs.

Semidefinite programming bounds on fractional cut-cover and maximum 2-SAT for highly regular graphs