Construction of 3-GDDs with block size 4 and 2 groups using 1 and 2 factorizations of complete graphs.

Abstract

Recently, we presented a construction of 3-GDD of block size four and two groups using 3-designs and Steiner quadruple systems and established that necessary conditions are sufficient for existence of 3-GDDs of block size 4 and 2 groups with the indices of the first and second associate pairs as 9 and 1 respectively are sufficient for n is equivalent to 3 mode 6 and n not equat to 3. In this paper we present the construction of 3_GDDs oof block size 4 and 2 groups using cycling a 1 and 2 factorizations of complete graphs.