Some decomposition of Directed Balanced Ternary Designs

• Main Authors: Bo-ting Shen, 沈勃廷
• Other Authors: Wen-Chung Huang
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/80722387830485518958

碩士 === 東吳大學 === 數學系 === 94 === Let Dv be the complete directed graph on v vertices and the graph Dv+ obtained by attaching a loop to each vertex of Dv. A directed balanced ternary design of order v is a pair (V, B), where V is a v-set and B is a collection of ordered triples of elements in V (each triple may have repeated 0, 1, 2 elements), such that every ordered pair of distinct elements of V appear twice. In this paper we will show the DBTD(v;ρ2;3,2) decomposition when ρ2 = 1, 2, 3. We use the embedding methods to show (i) There exists a decomposition of DBTD(v;1;3,2) when v ≡ 0 or 2 (mod 3) and v ≧ 2. (ii) There exists a decomposition of DBTD(v;2;3,2) when v ≡ 0 (mod 3) and v ≧ 3. (iii) There exists a decomposition of DBTD(v;3;3,2) when v ≡ 0 or 1 (mod 3) and v ≧ 4.