New Bounds on Graph Energy via Topological Indices

This paper establishes a comprehensive framework of novel upper bounds for the energy of graphs, rigorously connecting this spectral invariant to a suite of topological indices. We derive a unified collection of theorems that express graph energy in terms of fundamental parameters-order, size, and extreme degrees-while intricately incorporating advanced indices such as the general zeroth-order Randić index, the Sombor index, and the atom-bond connectivity index. Our results not only generalize but also systematically refine many classical bounds in the literature, demonstrating the profound interplay between spectral graph theory and chemical graph theory.