Algebraic Graph Theory - Maxwell Levit

Monday, February 12, 2024 11:30 am - 12:30 pm EST (GMT -05:00)

Title: Subconstituents of DracknsĀ 

Speaker: Maxwell Levit
Affiliation: Simon Fraser University
Location: Please contactSabrina Latofor Zoom link.

Abstract: For a distance-regular graph X and an arbitrary vertex v, we often find interesting structure in the subgraph of X induced on vertices at distance 2 from v.

For example:

Any strongly-regular graph with parameters (n,k,a,k/2) can be found at distance 2 from a vertex in a distance-regular graph of diameter 3.

Certain distance-regular graphs of diameter 3 can be found at distance 2 from a vertex in a Moore graph of girth 5.

These (and more) examples are known as second-subconstituents, and they can be studied using the Terwilliger (or subconstituent) algebra of X. I will discuss this theory in the case that X is a distance-regular antipodal cover of a complete graph (drackn). This setting generalizes the first example and includes the second.

I will describe some general techniques for studying the Terwilliger algebras of drackns and then restrict to drackns without triangles. In this setting I will explain how to compute the spectrum of the second-subconstituent of any triangle-free drackn, except possibly the second-subconstituent OF a second-subconstituent of a Moore graph of valency 57.