IJPAM: Volume 81, No. 1 (2012)

GROUP DIVISIBLE DESIGNS WITH TWO
ASSOCIATE CLASSES AND WITH TWO UNEQUAL GROUPS

Nittiya Pabhapote
School of Science and Technology
University of the Thai Chamber of Commerce
Dindaeng, Bangkok, 10400, THAILAND


Abstract. A group divisible design $\GDD(m, n; 3, \lambda_1, \lambda_2)$ is an ordered triple $(V, G, \B),$ where $V$ is a $m+n$-set of symbols, $G$ is a partition of $V$ into $2$ sets of sizes $m, n$, each set being called group, and $\B$ is a collection of $3$-subsets (called blocks) of $V$, such that each pair of symbols from the same group occurs in exactly $\lambda_1$ blocks; and each pair of symbols from different groups occurs in exactly $\lambda_2$ blocks. In this paper, we find necessary and sufficient conditions for the existence of a $\GDD(m, n; 3, \lambda_1, \lambda_2)$ with $\lambda_1 \geq \lambda_2$.

Received: August 19, 2012

AMS Subject Classification: 05B05, 05B07

Key Words and Phrases: graph decomposition, group divisible design

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 1