Spectral Graph Theory

Course offered at UFMG in 2021.2


Instructor: Gabriel Coutinho


Classes: Tuesdays & Thursdays / 13h-14h40 (BRT) / lectures on MS Teams

Playlist with past lectures


Course syllabus (in Portuglish)


Course notes (to be updated constantly)


Assignments

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Tentative schedule

19/10/2021 – Power series and generating functions
21/10/2021 – Symmetric matrices
26/10/2021 – Adjacency matrix of a graph
28/10/2021 – Some eigenvalue results
02/11/2021 – HOLIDAY
04/11/2021 – More eigenthings
09/11/2021 – Graph Isomorphism
11/11/2021 – Graph Isomorphism
16/11/2021 – Walks
18/11/2021 – Characteristic polynomial
23/11/2021 – Reconstruction
25/11/2021 – Matching polynomial
30/11/2021 – Matching polynomial
02/12/2021 – Covers / detour to Sensitivity Conjecture
07/12/2021 – Interlacing families
09/12/2021 – Interlacing families
14/12/2021 – Rayleigh Quotients
16/12/2021 – Interlacing
20/12..02/01 – Christmas break
04/01/2022 – Bounds on alpha and chi
06/01/2022 – Bounds on alpha and chi
11/01/2022 – Linear and integer optimization
13/01/2022 – Semidefinite optimization and theta number
18/01/2022 – Theta function
20/01/2022 – Theta function and variants
25/01/2022 – Laplacian matrix – physical processes
27/01/2022 – Trees and representations
01/02/2022 – Partitioning
03/02/2022 – Partitioning
08/02/2022 – Nodal domains
10/02/2022 – Inertia and trees
15/02/2022 – Minimum rank and planarity