  Graph states possess significant practical value in measurement-based quantum
computation, with complete graph states that exhibit exceptional performance in
quantum metrology. In this work, we introduce a method for generating
multiparticle complete graph states using a spin-$1/2$ Heisenberg $XX$ chain
subjected to a time-varying magnetic field, which applies to a wide range of
systems. Our scheme relies exclusively on nearest-neighbor interactions between
atoms, with real-time magnetic field formation facilitated by quantum optimal
control theory. We focus specifically on neutral-atom systems, finding that
multiparticle complete graph states with $N=3\sim6$ can be achieved in less
than $0.25~\mu{\rm s}$, utilizing a hopping amplitude of ${J}/{(2\pi)} =
-2.443~{\rm MHz}$. This assumes an initial state provided by an equal-weight
superposition of all spin states that are encoded by the dipolar interacting
Rydberg states. Additionally, we thoroughly address various experimental
imperfections and showcase the robustness of our approach against atomic
vibrations, fluctuations in pulse amplitude, and spontaneous emission of
Rydberg states. Considering the common occurrence of disturbances in
experimental setups of neutral-atom systems, our one-step strategy for
achieving such graph states emerges as a more empirically viable alternative to
techniques based on controlled-Z gates.
