A comparison of the Delsarte and Lovász bounds

Delsarte's linear programming bound (an upper bound on the cardinality of cliques in association schemes) is compared with Lov\acute{a}sz's \theta -function bound (an upper bound on the Shannon capacity of a graph). The two bounds can be treated in a uniform fashion. Delsarte's linear programming bound can be generalized to a bound \theta \prime(G) on the independence number \propto(G) of an arbitrary graph G , such that \theta \prime(G) \leq \theta(G) . On the other hand, if the edge set of G is a union of classes of a symmetric association scheme, \theta(G) may be calculated by linear programming, For such graphs the product \theta(G) . \theta(G) is equal to the number of vertices of G .