Certain 3-decompositions of complete graphs, with an application to finite fields

Citation

Rowlinson P (1985) Certain 3-decompositions of complete graphs, with an application to finite fields. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 99 (3-4), pp. 277-281. https://doi.org/10.1017/S0308210500014293

Abstract
A necessary condition is obtained for a complete graph to have a decomposition as the line-disjoint union of three isomorphic strongly regular subgraphs. The condition is used to determine the number of non-trivial solutions of the equation x3+y3 = z3 in a finite field of characteristic p ≡ 2 mod 3.

Journal
Proceedings of the Royal Society of Edinburgh: Section A Mathematics: Volume 99, Issue 3-4