#### Date of Graduation

Summer 2015

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Cameron Wickham

#### Keywords

Laplacian matrix, eigenvalues, spectra, characteristic function, graph theory, spectral graph theory

#### Subject Categories

Mathematics

#### Abstract

Spectral graph theory has started to gain popularity and usefulness in describing graphs using algebraic tools. Specifically the Laplacian matrix has been found to have rather nice eigenvalues with several applications to include the behavior of electricity, liquids, and Gaussian molecules. We explicitly state the characteristic equation and eigenvalues for the Laplacian matrix of zero divisor graphs of rings of the form ℤ! where � is prime.

#### Copyright

© William A. Jones

#### Recommended Citation

Jones, William A., "The Characteristic Polynomial of the Laplacian Matrix of Certain Zero-Divisor Graphs" (2015). *MSU Graduate Theses*. 1658.

http://bearworks.missouristate.edu/theses/1658