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On maximal cliques of Cayley graphs over fields
classification
math.CO
keywords
graphsmaximalcayleycliquesorderpaleyadditiveclass
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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.
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