On maximal cliques of Cayley graphs over fields
Abstract
We describe a new class of maximal cliques, with a vector space structure, of Cayley graphs defined on the additive group of a field. In particular, we show that in the cubic Paley graph with order q3, the subfield with q elements forms a maximal clique. Similar statements also hold for quadruple Paley graphs and Peisert graphs with quartic order.
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