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GDDs with two associate classes and with one group of size 1 and m groups of size n and λ_1=5,λ_2=1 |
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| รหัสดีโอไอ | |
| Creator | Wannee Lapchinda |
| Title | GDDs with two associate classes and with one group of size 1 and m groups of size n and λ_1=5,λ_2=1 |
| Contributor | Avapa Chantasartrassmee, Aisuriya Sudprasert |
| Publisher | Faculty of Science, Khon Kaen University |
| Publication Year | 2568 |
| Journal Title | KKU Science Journal |
| Journal Vol. | 53 |
| Journal No. | 2 |
| Page no. | 185-190 |
| Keyword | Group divisible designs, Balanced incomplete block design, Graph decomposition |
| URL Website | https://ph01.tci-thaijo.org/index.php/KKUSciJ |
| Website title | Thai Journal Online (ThaiJO) |
| ISSN | 3027-6667 |
| Abstract | A group divisible design GDD(v=1+n+n+⋯+n,1+m,3,λ_1,λ_2) is an ordered pair (V,B) where V is an (1+mn)- set of symbols and B is a collection of 3- subsets (called blocks) of V satisfying the following properties: the (1+mn)- set is divided into 1 group of size 1 and m groups of size n; each pair of symbols from the same group occurs in exactly λ_1 blocks in B; and each pair of symbols from different groups occurs in exactly λ_2 blocks in B. In this paper, we find necessary and sufficient conditions for the existence of a group divisible design group divisible design GDD(v=1+n+n+⋯+n,1+m,3,5,1), where m,n ≥3. |
