17 January 2023
Paley-type graphs link number theory and graph theory
The number of size 3 cliques depends on properties of the prime factors
Size 4 cliques are determined by solutions to a quadratic equation
Formulas for clique numbers do not involve advanced mathematics like character sums or Jacobi sums
Uncovering hidden structures: A guide to cliques in Paley-type graphs
This paper studies cliques, fully connected subgraphs, in Paley-type graphs, a family of graphs that connect number theory and graph theory. The authors derive combinatorial formulas for cliques of sizes 3 and 4. Their approach appeals to a general audience by avoiding technicalities, focusing on key insights, and using examples.
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