The goal of this project is to analyze families of small graphs with one or two loops at various vertices. We examine their adjacency matrices and Kronecker Products and determine their corresponding spectra. We describe features of the graphs and derive the number of closed walks. The degrees of each vertex, expressions for the spectra of each graph, and the correlating multiplicities of the eigenvalues were found through pattern recognition and implementation of the Binomial Theorem and a generating function.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Logan-Rung, Joshua J.

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042220-154555

Advisor

• Christopher, Peter R.

Year

• 2020

Date created

• 2020-04-22

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright