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- W2294661513 abstract "In this paper, we investigate the isoperimetric constant (or expansion constant) of a Paley graph, and the Kazhdan constant of the group and generating set associated with a Paley graph. We give two new upper bounds for the isoperimetric constant h(Xp) for the Paley graph Xp. These bounds improve previously known eigenvalue bounds on h(Xp). Along with a known eigenvalue lower bound for h(Xp), they provide a narrow strip in which h(Xp) must live. More precisely, we show that (p −p)∕4 ≤ h(Xp) ≤ (p − 1)∕4, which implies that limp→∞h(Xp)∕p = 1∕4. In addition, we show that the Kazhdan constant associated with the integers modulo p and the generating set for the Paley graph Xp approaches 2 as p tends to infinity, which is the best possible limit that the Kazhdan constant can be." @default.
- W2294661513 created "2016-06-24" @default.
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- W2294661513 date "2016-03-02" @default.
- W2294661513 modified "2023-09-27" @default.
- W2294661513 title "The isoperimetric and Kazhdan constants associated to a Paley graph" @default.
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- W2294661513 doi "https://doi.org/10.2140/involve.2016.9.293" @default.
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