Q4-factorization of λ kn and λ kx(m)

Abstract

In this study, we show that necessary conditions for Q4- factorization of λKn and λKx(m) (complete x partite graph with parts of size m) are sufficient. We proved that there exists a Q4-factorization of λKx(m) if and only if mx 0 (mod 16) and λm(x - 1) 0 (mod 4). This result immediately gives that λKn has a Q4-factorization if and only if n 0 (mod 16) and λ 0 (mod 4). © 2020 University of Calgary. All rights reserved.