The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters

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The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters

Brouwer, Andries E.; Cioabă, Sebastian M.; Ihringer, Ferdinand; McGinnis, Matt

Journal of combinatorial theory. Series B, November 2018, 2018-11-00, Volume: 133

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We prove a conjecture by Van Dam & Sotirov on the smallest eigenvalue of (distance-j) Hamming graphs and a conjecture by Karloff on the smallest eigenvalue of (distance-j) 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 P- and Q-polynomial association schemes.

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Brouwer, Andries E. | Cioabă, Sebastian M. | Ihringer, Ferdinand | McGinnis, Matt

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