Construction and Intersection of Long-Kite Design

• Main Authors: Yu-Zhi Liang, 梁育誌
• Other Authors: Wen-Chung Huang
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/16129615077217040186

碩士 === 東吳大學 === 數學系 === 99 === A long-kite graph is a triangle with a tail consisting of a path of length 2. Let G be a graph. A long-kite design of G is a collection of subgraphs of G, the subgraph is isomorphic to a long-kite graph, such that those subgraphs form a partition of G. A long-kite design of order n is a long-kite design of Kn. The main content of this report discuss some property about the long-kite design of order n. In section 1, we introduce some basic definition which will be used later in this article. In section 2, we discuss the case that Kn can be decomposed into long-kite graphs completely. In this section, we divide three parts. In part 1, for orders 6, 10, 11, 15, 20, 21, 25, graphs K15\K5 and K25\K5, we give the small cases, then exchange the digits in every orders and discuss the number of intersections. In part 2, we make the construction for the general order 10k, 10k+1, 10k+5 and 10k+6. In part 3, from part 1 and part 2, we show that the spectrum for the pairwise disjoint intersection of long-kite designs of order n is the set {0, 1, 2, …, [n/5]}. In section 3, we discuss the case when Kn can not be decomposed into long-kite graphs completely. We divide four parts in this section. In part 1, we give the necessary condition of long-kite design of λＫn. In part 2, for certain order such as 7, 8, 9, 12, 13, 14, 22, 23, 24, we give the small cases. In part 3, we give the construction for the order 10k+2, 10k+3, 10k+4, 10k+7, 10k+8 and 10k+9. In part 4, we find the method that can decompose compeletely and give a long-kite design of λＫn.