IJPAM: Volume 71, No. 3 (2011)

GROUP DIVISIBLE DESIGNS WITH
TWO ASSOCIATE CLASSES AND $\lambda_2=3$

Arjuna Chaiyasena$^1$, Nittiya Pabhapote$^2$
$^1$School of Mathematics
Suranaree University of Technology
Nakhon Ratchasima, 30000, THAILAND
$^2$School of Science and Technology
University of the Thai Chamber of Commerce
Dindaeng, Bangkok, 10400, THAILAND


Abstract. Necessary and sufficient conditions for the existence of Group divisible designs with two groups of unequal sizes and block size tree with $\lambda_{2} = 3$, $\lambda_{1} \geq 3$ are here considered. We find that the necessary conditions, derived from graph theoretic conditions, are sufficient as well. We present some constructions to prove sufficiency.

Received: June 3, 2011

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: 2011
Volume: 71
Issue: 3