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

12 pages, revised based on referees' suggestions

References in corpus (2)

• On the clique number of Paley graphs of prime power order
• On the directions determined by Cartesian products and the clique number of generalized Paley graphs

Cited by in corpus (5)

• Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields
• On eigenfunctions and maximal cliques of generalised Paley graphs of square order
• Maximality of subfields as cliques in Cayley graphs over finite fields
• Gauss sums and the maximum cliques in generalized Paley graphs of square order
• The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes