In this research, we explore the subject of graph energy. We first discuss the connections between linear algebra and graph theory and review some important definitions and facts of these two fields. We introduce graph energy and provide some historical perspectives on the subject. Known results of graph energy are also mentioned and some relevant results are proven. We discuss some applications of graph energy in the physical sciences. Then, Randic energy is defined and results are given and proved for specific families of graphs. We focus on simple, connected graphs that are commonly studied in graph theory. Also, the Laplacian energy of a graph is defined. We then examine the connections between the different types of energies for graphs, beginning with graph energy and Randic energy, followed by Laplacian energy and Randic energy. In our results chapter, we introduce the Petersen graph and calculate the Randic energy of this graph. We also define Stacked-Book graphs and perform some calculations on these graphs. From these calculations, we form a conjecture and discuss some details on how to proceed with the proof of this conjecture. Finally, we summarize our work and details are provided on how this research can be continued.
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Mohapatra, Ram N.
Master of Science (M.S.)
College of Sciences
Length of Campus-only Access
Masters Thesis (Campus-only Access)
Burns, Brittany, "On Randic Energy of Graphs" (2016). Electronic Theses and Dissertations, 2004-2019. 5223.