7 February 2021
Paley graphs have maximal cliques of size q or q+r(q)
Two constructions yield cliques of size q+r(q)
Linear mappings connect the clique sets
The mappings are bijections and involutions
Results contribute to open problems on Paley graph structure
Unlocking the Secrets of Maximal Cliques in Paley Graphs
This paper establishes a correspondence between two types of maximal cliques in Paley graphs, which are important in graph theory and have applications in coding theory and cryptography. The authors reinterpret prior constructions and introduce linear mappings that link clique sets of the same size. Their findings reveal deep connections in these graphs and provide insight into their structural properties.
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