Discrepancy and eigenvalues of Cayley graphs

May 29, 2018

Yoshiharu Kohayakawa, Vojtěch Röd and Mathias Schacht

We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.

The whole paper is available here.

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