X-Ramanujan Graphs - Ex Uno Plures

Explore the fascinating world of X-Ramanujan graphs in this computer science and discrete mathematics seminar presented by Ryan O'Donnell from Carnegie Mellon University. Delve into the concept of "ex uno plures" (from one, many) as it applies to graph theory. Begin with an introduction and motivation behind the topic, then progress through key definitions and concepts such as additive lifts, generic graphs, and vertex-transitive graphs. Examine eigenvalues and learn techniques for finding the maximum root and alpha polynomial. Investigate matching polynomials and sum graphs, gaining insight into their combinatorial interpretation. Conclude with a comprehensive overview of the seminar's main points and their implications in the field of graph theory and computer science.

Intro
Motivation
Definition
Additive lifts
Generic graphs
Vertextransitive graphs
Eigenvalues
Finding the maximum root
Finding the alpha polynomial
Matching polynomials
Sum graphs
combinatorial interpretation
conclusion