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)
12 - Tensor and Cartesian products (PDF; Vimeo; YouTube)
13 - Characteristic polynomial + cycle decompositions (PDF; Vimeo; YouTube)
14 - Coalescing; introduction to Laplacian (PDF; Vimeo; YouTube)
15 - Properties of Laplacian, including joins (PDF; Vimeo; YouTube)
16 - Matrix Tree Theorem (PDF; Vimeo; YouTube)
17 - A few more comments about Laplacian; introduction to signless Laplacian (PDF; Vimeo; YouTube)
18 - Signless Laplacian and line graphs (PDF; Vimeo; YouTube)
19 - Comments about hypercubes, start of probability transition matrix (PDF; Vimeo; YouTube)
20 - Stationary distribution of random walks (PDF; Vimeo; YouTube)
21 - Normalized Laplacian vs. other matrices (PDF; Vimeo; YouTube)
22 - Some practice with harmonic eigenvectors (PDF; Vimeo; YouTube)
23 - Normalized Laplacian and equitable partitions (PDF; Vimeo; YouTube)
24 - Singular values and discrepancy (PDF; Vimeo; YouTube)
25 - Discrepancy and Cheeger constants (PDF; Vimeo; YouTube)
26 - Kemeny's constant (PDF; Vimeo; YouTube)
27 - Introduction to distance matrices (PDF; Vimeo; YouTube)
28 - How graph labeling naturally connects with distance matrices (PDF; Vimeo; YouTube)
29 - A quick comment about interlacing and chromatic numbers (PDF; Vimeo; YouTube)