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