Abstract
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 Krational 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
