On maximal cliques of Cayley graphs over fields

摘要

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 q(3), the subfield with q elements forms a maximal clique. Similar statements also hold for quadruple Paley graphs and Peisert graphs with quartic order.