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We study the reciprocal of the mean quantum Fisher information (RMQFI),$\chi^2$ for general three qubit states, having graph and hypergraph states asspecial cases, for identifying genuine multi party entanglement characterizedby $\chi^2 <1$. We demonstrate that the most symmetric graph state and the GHZstate have the lowest RMQFI values leading to the highest statistical speedshowing that both these states attain the Heisenberg limit in phasesensitivity. Unlike the GHZ state, graph states have the same RMQFI values formeasurement through different parameters, a property shared by the hypergraphstates. Three qubit graph and hypergraph states can violate Bell's inequalityas $F_Q > N$. Both the GHZ state and the most symmetric graph state have thehighest concurrence equalling 3 and the maximum QFI values.

Achieving Heisenberg limit in the phase measurement through three-qubit graph states