Geodesic
Discrepancy and eigenvalues of Cayley graphs
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 941-954

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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.
DOI : 10.1007/s10587-016-0302-x
Classification : 05C50, 05C80
Keywords: eigenvalue; discrepancy; quasirandomness; Cayley graph 
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     title = {Discrepancy and eigenvalues of {Cayley} graphs},
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     pages = {941--954},
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Kohayakawa, Yoshiharu; Rödl, Vojtěch; Schacht, Mathias. Discrepancy and eigenvalues of Cayley graphs. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 941-954. doi: 10.1007/s10587-016-0302-x

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