The Degree Energy of a Graph

A. R. Nagalakshmi, A. S. Shrikanth, G. K. Kalavathi and K. S. Sreekeshava ()
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A. R. Nagalakshmi: Department of Mathematics, Malnad College of Engineering, Affiliated to Visvesvaraya Technological University, Belagavi 590018, India
A. S. Shrikanth: Department of Mathematics, Adichunchanagiri Institute of Technology, Affiliated to Visvesvaraya Technological University, Belagavi 590018, India
G. K. Kalavathi: Department of Mathematics, Malnad College of Engineering, Affiliated to Visvesvaraya Technological University, Belagavi 590018, India
K. S. Sreekeshava: Jyothy Institute of Technology, Affiliated to Visvesvaraya Technological University, Belagavi 590018, India

Mathematics, 2024, vol. 12, issue 17, 1-15

Abstract: 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.

Keywords: degree matrix; degree spectra; degree energy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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