Q(5)-factorization of lambda K-n

Abstract

Q(k) is the simple graph whose vertices are the k-tuples with entries in {0, 1} and edges are the pairs of k-tuples that differ in exactly one position. In this paper, we proved that there exists a Q(5)-factorization of lambda K-n if and only if (a) n equivalent to 0(mod 32) if lambda equivalent to 0(mod 5) and (b) n equivalent to 96(mod 160) if lambda not equivalent to 0(mod 5).