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Discrete Math

The smallest eigenvalues of some Hamming and Johnson graphs

Sebastian Cioaba, U. Delaware

Location:  Hill 705
Date & time: Monday, 30 April 2018 at 2:00PM - 3:00PM

  Abstract:  The smallest eigenvalue of a graph 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 some of the 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 outline our proofs of a 2016 conjecture by Van Dam and Sotirov on the smallest eigenvalue of (distance-j) Hamming graphs and a 1999 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.

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