Spectral graph theory class (2023)

This page contains the lecture recordings, homeworks, and exams that were used for the Spectral graph theory course taught at Iowa State University in Fall 2023.

Lectures (Fall 2023)

01 - Brief overview of spectral graph theory; review of some linear algebra (PDF; Vimeo; YouTube)

02 - End of linear algebra; some basics of graph theory (PDF; Vimeo; Youtube)

03 - Introduction to adjacency matrix; eigenvalues of cycle / circulant matrices (PDF; Vimeo; YouTube)

04 - Eigenvalues of path / complete bipartite graph; symmetry of eigenvalues (PDF; Vimeo; YouTube)

05 - Adjacency matrix as walk counting matrix; Perron-Frobenius Theorem (PDF; Vimeo; YouTube)

06 - Eigenvalues of complement of regular graph; join of two regular graphs (PDF; Vimeo; YouTube)

07 - Relationship between number of eigenvalues and diameter; automorphisms for graphs with distinct eigenvalues (PDF; Vimeo; YouTube)

08 - Equitable partitions (PDF; Vimeo; YouTube)

09 - Strongly regular graphs (PDF; Vimeo; YouTube)

10 - (Double) covers of graphs (PDF; Vimeo; YouTube)

11 - Switching (Seidel and Godsil-McKay) (PDF; Vimeo; YouTube)

Homeworks (Fall 2023)

Material from the 2017 iteration of the spectral graph theory class