Decomposition of Graphs into Extended Directed triples

• Main Authors: Cheng-ta Hsieh, 謝政達
• Other Authors: Huang-Chung Wen
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/07941099790489085970

碩士 === 東吳大學 === 數學系 === 93 === Abstract An extended directed triple system of the order n, EDTS(n), is a pair (V, B), where B is a collection of ordered triples from an n-set V (each ordered triple may have repeated elements) such that every ordered pair of elements of V, not necessarily distinct, is contained in exactly one ordered triple of B. The elements of B are called blocks. There are five types of blocks: (1) [a, b, c], (2) [a, b, a], (3) [a, a, b], (4) [ b, a, a], (5) [a, a, a] (in which it is the set of ordered pairs {ab, bc, ac}, {ab, ba, aa}, {aa, ab}, {ba, aa} and {aa}, respectively). Let b3, b2, b1, b0 denote the number of blocks of (V,B) that are of the type (1), (2), (3) or (4), (5), respectively. Evidently b3 and b0 are determined by b2 and b1. In this paper, we will discuss the decomposition of λDv+，λDv++，λDv+++ into transitive triples, loops and lollipops of type (2) in section 2 and lollipops of type (3) or (4) in section 3.