Christopher, Peter R.
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.
Worcester Polytechnic Institute
Major Qualifying Project
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