  Violation of a Bell inequality guarantees the existence of quantum
correlations in a quantum state. A pure bipartite quantum state, having
nonvanishing quantum correlation, always violates a Bell inequality. Such
correspondence is absent for multipartite pure quantum states. For a shared
multipartite quantum state, we establish a connection between the monogamy of
Bell inequality violation and genuine multi-site entanglement as well as
monogamy-based multiparty quantum correlation measures. We find that
generalized Greenberger-Horne-Zeilinger states and another single-parameter
family states which we refer to as the "special Greenberger-Horne-Zeilinger"
states have the status of extremal states in such relations.
