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Quantum discord, an information-theoretic quantum correlation measure, cansatisfy as well as violate monogamy, for three-party quantum states. Wequantify the feature using the concept of discord monogamy score. We find anecessary condition of a vanishing discord monogamy score for arbitrarythree-party states. A necessary and sufficient condition is obtained for purestates. We prove that the class of states having a vanishing discord monogamyscore cannot have arbitrarily high genuine multipartite entanglement, asquantified by generalized geometric measure. In the special case of three-qubitpure states, their classification with respect to the discord monogamy score,reveals a rich structure that is different from that which had been obtained byusing the monogamy score corresponding to the entanglement measure calledconcurrence. We investigate properties like genuine multipartite entanglementand violation of the multipartite Bell inequality for these states.

Characterization of Tripartite Quantum States with Vanishing Monogamy Score