  In the SU(2) dynamics, it is especially significant to achieve a simultaneous
optimal multiparameter estimation but it is very difficult. Evolution on SU(N)
dynamics is a research method to explore simultaneous multiparameter estimation
with the quantum network. As the highly entangled states, graph state, is an
intrinsical quantum resource for quantum metrology. For n-qubit graph state, we
propose a simultaneous multiparameter estimation scheme that investigates
evolution in SU(N) dynamics. For single-parameter estimation, the precision
limit beyond the Heisenberg limit in the higher dimension spin of SU(2). We
consider two scenarios where the Hamiltonian operator is commutation and
non-commutation respectively and verify that the global estimation precision is
higher than the local estimation precision. In the parameter limit condition,
the precision of parameter estimation for the simultaneous estimation of each
parameter is equal to the precision of the singleparameter estimation. In
addition, we find a precision-enhancement scheme that depends on the dynamics
SU(N). The smaller the N for the dynamics evolution, the higher the precision
of the parameter estimation. Finally, we prove that the graph state is the
optimal state of quantum metrology, a set of optimal measurement basic can be
found, and the precision limit of multiparameter estimation can attain the
quantum Cram\'er-Rao bound.
