On maximal cliques of Cayley graphs over fields
Chi Hoi Yip
TL;DR
This paper introduces a new class of maximal cliques with vector space structure in Cayley graphs over fields, highlighting their properties in Paley and Peisert graphs of specific orders.
Contribution
It identifies and characterizes a novel class of maximal cliques with algebraic structure in Cayley graphs over fields, including specific examples in Paley and Peisert graphs.
Findings
Subfield with q elements forms a maximal clique in cubic Paley graphs.
Similar maximal cliques exist in quadruple Paley and Peisert graphs.
Maximal cliques have a vector space structure within these Cayley graphs.
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 , the subfield with elements forms a maximal clique. Similar statements also hold for quadruple Paley graphs and Peisert graphs with quartic order.
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