Let p be a prime number congruent to 1 (mod 4) and let K be a finite field with p elements. The Paley graph P(p) is the graph having vertex set K where two vertices are joined when their difference is a square in the finite field.

The purpose of this talk is to show that counting the number of complete subgraphs in P(p) can be reduced to counting the number of K-rational points of a certain projective variety. We will apply this formulation to reproduce the known formula for the number of complete subgraphs of order 4 in P(p).

Last Updated: October 4 2004 by Hirotachi Abo