Global properties, fractality, and mass segregation in single, paired, and grouped open clusters

Context. Open clusters (OCs) provide key insights into the formation and dynamical evolution of stellar systems. While many studies have focused on individual clusters, the influence of environmental factors on their structural properties remains an open question. Aims. We investigate the structural and dynamical properties of OCs classified as single, in pairs, or in groups. By analysing their mass, size, age, fractality, and mass segregation, we aim to identify systematic differences among these categories and assess the role of the Galactic environment in their evolution. Methods. We analysed a sample of 420 single OCs, 415 in pairs, and 317 in groups, with total masses 2.2 ≤ log(M/Mʘ) ≤ 3.7. To characterise their structure, we applied the Q parameter, which differentiates fractal from radial distributions. Additionally, we calculated the local density ratio to quantify the mass segregation and explore its dependence on cluster environment. Results. OCs in groups tend to be the youngest, followed by those in pairs and then single OCs. Although sizes are similar, OCs in pairs and groups tend to be less concentrated. Structurally, grouped OCs exhibit the highest fractality, which decreases with age as clusters evolve towards more radial configurations. Mass segregation is observed in 80% of OCs, with a marginally higher incidence in single clusters. Some older single OCs show inverse segregation, with massive stars at larger radii. Spatially, single OCs are more dispersed, whereas paired and grouped OCs are concentrated in spiral arms and active star-forming regions. Conclusions. OC evolution appears to be influenced by a combination of internal dynamics and environmental factors. Single OCs tend to exhibit characteristics consistent with more advanced dynamical evolution, whereas those in pairs and groups may retain structural features that reflect their formation environment. The presence of substructures and fractality in younger clusters suggests that interactions within their birth environment play a crucial role in shaping their long-term development. More massive OCs evolve towards radial configurations, while less massive ones may retain fractal characteristics for longer periods. These findings support the idea that both intrinsic properties and external environmental factors play a role in shaping the evolution of OCs.