The smallest eigenvalue of graphs is closely related to other graph
parameters such as the independence number, the chromatic number or
the max-cut. In this talk, I will describe the well-known
connections between the smallest eigenvalue and the max-cut of a
graph that have motivated various researchers such as Karloff, Alon,
Sudakov, Van Dam, Sotirov to investigate the smallest eigenvalue
of Hamming and Johnson graphs. I will describe our proofs of a
conjecture by Van Dam and Sotirov on the smallest eigenvalue of
(distance-j) Hamming graphs and a conjecture by Karloff on the
smallest eigenvalue of (distance-j) Johnson graphs and mention some
open problems. This is joint work with Andries Brouwer, Ferdinand
Ihringer and Matt McGinnis.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
The ACO Seminar (2018–2019)