The Degree Energy of a Graph

The incidence of edges on vertices is a cornerstone of graph theory, with profound implications for various graph properties and applications. Understanding degree distributions and their implications is crucial for analyzing and modeling real-world networks. This study investigates the impact of vertex degree distribution on the energy landscape of graphs in network theory. By analyzing how vertex connectivity influences graph energy, the research enhances the understanding of network structure and dynamics. It establishes important properties and sharp bounds related to degree spectra and degree energy. Furthermore, the study determines the degree spectra and degree energy for several key families of graphs, providing valuable insights with potential applications across various fields.