Some colouring problems for Paley graphs

The Paley graph PqPq, where q≡1(mod4) is a prime power, is the graph with vertices the elements of the finite field FqFq and an edge between x and y   if and only if x-yx-y is a non-zero square in FqFq. This paper gives new results on some colouring problems for Paley graphs and related discussion.