  In this article the robustness of tripartite Greenberger-Horne-Zeilinger
(GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM)
interaction. We consider a closed system of three qubits and an environmental
qubit. The environmental qubit interacts with any one of the three qubits
through DM interaction. The tripartite system is initially prepared in GHZ and
W states respectively. The composite four qubits system evolve with unitary
dynamics. We detach the environmental qubit by tracing out from four qubits and
profound impact of DM interaction is studied on the initial entanglement of the
system. As a result we find that the bipartite partitions of W states suffer
from entanglement sudden death (i.e. ESD), while tripartite entanglement does
not. On the other hand bipartite partitions and tripartite entanglement in GHZ
states does not feel any influence of DM interaction. So, we find that GHZ
states have robust character than W states. In this work we consider
generalised GHZ and W states and three $\pi$ is used as an entanglement
measure. This study can be useful in quantum information processing where
unwanted DM interaction takes place.
