Lagrangeʹs Theorem and Integrality for Finite Commutative Hypergroups with Applications to Strongly Regular Graphs Original Research Article

We introduce a notion of integrality, or resonance, for finite commutative hypergroups and their generalizations, signed hypergroups. Lagrangeʹs theorem for subhypergroups is established using a condition of integrality of weights for the dual signed hypergroup. Order three hypergroups are studied and resonant ones whose duals have integral weights are classified. Applications are given to the theory of strongly regular graphs.