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 Lovacute{a}sz\´s -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 on the independence number of an arbitrary graph , such that . On the other hand, if the edge set of is a union of classes of a symmetric association scheme, may be calculated by linear programming, For such graphs the product . is equal to the number of vertices of .