In this report, we investigated two questions in the field of spectral graph theory. The first question was whether it is possible to extend recent results to find a large class of graphs uniquely determined by the spectrum of its adjacency matrix. Our investigation led to the discovery of a pair of cospectral graphs which contradicted the existence of such a class. The second question was whether there exists a construction of cospectral graphs that consists of adding a single edge and vertex to a given pair of cospectral graphs. We discovered that such a construction exists, and generated several pairs of cospectral graphs using this method. Further investigation showed that this construction of cospectral graphs is related to two previously studied constructions.

• 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

• DiGenio, Anthony Joseph

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042811-121510

Advisor

• Christopher, Peter R.

Year

• 2011

Date created

• 2011-04-28

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright