The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters
Combinatorics
2018-04-23 v2 Discrete Mathematics
Abstract
We prove a conjecture by Van Dam and Sotirov on the smallest eigenvalue of (distance-) Hamming graphs and a conjecture by Karloff on the smallest eigenvalue of (distance-) Johnson graphs. More generally, we study the smallest eigenvalue and the second largest eigenvalue in absolute value of the graphs of the relations of classical - and -polynomial association schemes.
Keywords
Cite
@article{arxiv.1709.09011,
title = {The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters},
author = {Andries E. Brouwer and Sebastian M. Cioabă and Ferdinand Ihringer and Matt McGinnis},
journal= {arXiv preprint arXiv:1709.09011},
year = {2018}
}
Comments
30 pages, accepted by JCTB