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Title: Group divisible designs with two associate classes and λ 2 = 4
Authors: Uiyyasathian, C. 
Pabhapote, N. 
Keywords: Graph decomposition;Group divisible design
Issue Date: 2011
Publisher: Scopus
University of the Thai Chamber of Commerce
Source: C. Uiyyasathian, N. Pabhapote (2011) Group divisible designs with two associate classes and λ 2 = 4. International Journal of Pure and Applied Mathematics Vol.73 No.3, 289-298.
Abstract: A group divisible design GDD(v = v 1 + v 2 + · · · + v g,g, k, λ 1, λ 2) is an ordered triple (V, G, B), where V is a vset of symbols, G is a partition of V into g sets of size v 1, v 2,⋯ v g, each set being called group, and B is a collection of ksubsets (called blocks) ofV, such that each pair of symbols from the same group occurs in exactly λ 1 blocks; and each pair of symbols from different groups occurs in exactly λ 2 blocks. Here, we focus on an existence problem of GDDs with two associate classes or when g = 2, and with blocks of size 3, when the required designs have two groups of unequal sizes and λ 2 = 4. We obtain the necessary conditions and prove that these conditions are sufficient.
Rights: This work is protected by copyright. Reproduction or distribution of the work in any format is prohibited without written permission of the copyright owner.
Appears in Collections:RSO: Journal Articles

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