The Hierarchical Structure of the Open Cluster NGC 752

The structure of open clusters provides key insights into their evolution and the dynamics of the Milky Way. Using Gaia DR3 data, we applied a hierarchical clustering algorithm to the open cluster NGC 752 based on the kinematical information and identified four substructures corresponding to different stages of disintegration. The cluster exhibits a pronounced signature of mass segregation. Its outer members show a clear expansion trend with a velocities of 0.25 $\rm{km~s^{-1}}$ in the plane of the sky. In addition, the system shows a projected rotational pattern with an angular velocity of approximately 0.03 $\rm{rad~Myr^{-1}}$. We also identified a correlation between the escape times of disturbed members and the epochs at which the cluster crossed the Galactic disk, highlighting the role of Galactic tidal forces in accelerating cluster dissolution. We conclude that hierarchical clustering based on projection bounding energy is effective for studying the internal structure of star clusters, but it has limitations when dealing with unconstrained structures such as tidal tails.