Discrepancy and Eigenvalues of Cayley Graphs
نویسندگان
چکیده
We consider quasirandom properties for Cayley graphs of finite abelian groups. In particular, we show that having uniform edgedistribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for Cayley graphs, even if they are sparse. This positively answers a question of Chung and Graham [“Sparse quasi-random graphs”, Combinatorica 22 (2002), no. 2, 217–244] for the particular case of Cayley graphs, while in general the answer is negative.
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تاریخ انتشار 2003