Decomposition of Graphs into Extended Directed triples
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,...
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ndltd-TW-093SCU054790012015-10-13T11:56:54Z http://ndltd.ncl.edu.tw/handle/07941099790489085970 Decomposition of Graphs into Extended Directed triples 圖分解為廣義有向三元集 Cheng-ta Hsieh 謝政達 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. Huang-Chung Wen 黃文中 2003 學位論文 ; thesis 43 en_US |
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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.
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author2 |
Huang-Chung Wen |
author_facet |
Huang-Chung Wen Cheng-ta Hsieh 謝政達 |
author |
Cheng-ta Hsieh 謝政達 |
spellingShingle |
Cheng-ta Hsieh 謝政達 Decomposition of Graphs into Extended Directed triples |
author_sort |
Cheng-ta Hsieh |
title |
Decomposition of Graphs into Extended Directed triples |
title_short |
Decomposition of Graphs into Extended Directed triples |
title_full |
Decomposition of Graphs into Extended Directed triples |
title_fullStr |
Decomposition of Graphs into Extended Directed triples |
title_full_unstemmed |
Decomposition of Graphs into Extended Directed triples |
title_sort |
decomposition of graphs into extended directed triples |
publishDate |
2003 |
url |
http://ndltd.ncl.edu.tw/handle/07941099790489085970 |
work_keys_str_mv |
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