Title

The Energy of Graphs

Document Type

Thesis

Publication Date

2010

Advisor

Thomas Sibley, Mathematics

Abstract

The topic of graph energy was first introduced by Ian Gutman in 1978 and arose as a problem in chemistry dealing with the -electron energy of a molecule. In chemistry, a molecule can be represented as a graph with vertices and edges where the vertices represent atoms and the edges represent bonds between the atoms. For a matrix associated with the graph, the energy of a graph is defined as the sum of the absolute value of the eigenvalues. For my thesis I focused on the relationship between two forms of energy, Laplacian energy and signless Laplacian energy, and tree graphs.

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