Graphs with three eigenvalues - Xiong, Zhiyuan (2019)
In this final year project, we have studied the graphs whose adjacency matrices have three distinct eigenvalues. There are mainly two topics studied in the project. First, in section 2, we focus on two interesting nonregular graphs with three distinct eigenvalues and three valencies. A technique, Godsil-McKay switching, which is able to construct cospectral graphs, is considered to explore the relationship between those two graphs mentioned above. Second, in section 3, we focus on Hermitian variety and a special family of graphs with three eigenvalues called multiplicative cones. The construction process of one multiplicative cone is described in details.