Infinite Paley graphs

Keywords: Paley graph, random graph, universal graph, quadratic residue, character sum

Abstract

Infinite analogues of the Paley graphs are constructed, based on uncountably many locally finite fields. By using character sum estimates due to Weil, they are shown to be isomorphic to the countable random graph of Erdős, Rényi and Rado.

Published
2020-08-06
Section
Groups and Graphs, Designs and Dynamics 2019