Faculty Advisor

Christopher, Peter R.

Abstract

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.

Publisher

Worcester Polytechnic Institute

Date Accepted

2020-04-22

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

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