Title

The Energy of Graphs

Document Type

Thesis

Publication Date

2010

Disciplines

Mathematics | Physical Sciences and Mathematics

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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