Generalized Paley graphs and their complete subgraphs of orders three and four

Madeline Locus Dawsey, Dermot McCarthy

Let $k\ge 2$ be an integer. Let $q$ be a prime power such that $q\equiv 1(\mathrm{mod}k)$ if $q$ is even, or, $q\equiv 1(\mathrm{mod}2k)$ if $q$ is odd. The generalized Paley graph of or…