Topological descriptors, entropy measures, and graph energy modeling in U-carbon allotropes.

The ability of carbon to adopt multiple hybridization states gives rise to a variety of allotropes with diverse electronic behaviors, including insulating, metallic, and potentially magnetic phases. Although metallic and magnetic structures have been explored, intrinsically ferromagnetic crystalline carbon allotropes remain rare. U-Carbon (UC), a recently synthesized crystalline allotrope with mixed sp2-sp3 hybridization, exhibits dynamic stability and intrinsic ferromagnetism under ambient conditions, highlighting its potential for next-generation materials. The aim of this study is to characterize the structural complexity of stacked UC configurations and investigate the relationships among their structural elements by applying degree and distance related topological indices together with entropy-derived measures. Furthermore, a regression model based on these indices is developed to efficiently determine graph energies in complex higher-dimensional structures, thereby providing a scalable computational framework.