In this paper a new parameter for hypergraphs called hypergraph infection is defined. This concept generalizes zero forcing in graphs to hypergraphs. The exact value of the infection number of complete and complete bipartite hypergraphs is determined. A formula for the infection number for interval hypergraphs and several families of cyclic hypergraphs is given. The value of the infection number for a hypergraph whose edges form a symmetric t-design is given, and bounds are determined for a hypergraph whose edges are a t-design. Finally, the infection number for several hypergraph products and line graphs are considered.

Abstract. We investigate strongly regular graphs for which Hoffman's ratio bound and Cvetcović's inertia bound are equal. This means that ve − = m − (e − − k), where v is the number of vertices, k is the regularity, e − is the smallest eigenvalue, and m − is the multiplicity of e − . We show that Delsarte cocliques do not exist for all Taylor's 2-graphs and for point graphs of generalized quadrangles of order (q, q 2 − q) for infinitely many q. For cases where equality may hold, we show that for nearly all parameter sets, there are at most two Delsarte cocliques.

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