Diameters of Cayley graphs of Chevalley groups

Authors:
M. Kassabov;T. R. Riley
Affiliations:
Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853, USA;Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853, USA
Venue:
European Journal of Combinatorics
Year:
2007

Citing 2
Cited 0

Some large trivalent graphs having small diameters

Discrete Applied Mathematics - Special double volume: interconnection networks
Concrete Math

Concrete Math

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Abstract

We show that for integers k=2 and n=3, the diameter of the Cayley graph of SL"n(Z/kZ) associated with a standard two-element generating set is at most a constant times n^2lnk. This answers a question of A. Lubotzky concerning SL"n(F"p) and is unexpected because these Cayley graphs do not form an expander family. Our proof amounts to a quick algorithm for finding short words representing elements of SL"n(Z/kZ). We generalize our results to other Chevalley groups over Z/kZ.