In this paper we analyse the center and centralizer of an element in the context of reversible regular hypergroups, in order to obtain the class equation in regular reversible hypergroups, by using complete parts. Af- ter an introduction in which basic notions and results of hypergroup theory are presented, particularly complete parts, then we give several properties, characterisations and also examples for the center and cen- tralizer of an element for two classes of hypergroups. The next para- graph is dedicated to hypergroups associated with binary relations. We establish a connection between several types of equivalence relations, in- troduced by J.Jantosciak, such as the operational relation, the insepara- bility and the essential indistin-guishability and the conjugacy relation for complete hypergroups. Finally, we analyse Rosenberg hypergroup associated with a conjugacy relation.
