Lecture

Expander Graphs: Properties and Eigenvalues

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In course

MATH-467: Probabilistic methods in combinatorics

The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...

Description

This lecture covers the concept of expanders and Ramanujan graphs, discussing their properties, eigenvalues, adjacency matrix, Laplacian matrix, and the relationship between d-regular graphs and eigenvalues. The instructor explains the construction of expanders, their expansion properties, and the spectral properties of Laplacian matrices. The lecture also delves into the existence of 1-sided and 2-sided Ramanujan sequences, the coloring of complete bipartite graphs, and the spectral expansion of graphs. The goal is to demonstrate the significance of expanders in graph theory and their applications in various fields.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

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