圖形之分割與反魔標號;Decompositions and Antimagic Labelings of Graphs

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/68875

Title:	圖形之分割與反魔標號;Decompositions and Antimagic Labelings of Graphs
Authors:	陳抮君;Chen,Zhen-Chun
Contributors:	數學系
Keywords:	圖形之分割;反魔標號;decompositions;antimagic
Date:	2015-07-24
Issue Date:	2015-09-23 14:45:46 (UTC+8)
Publisher:	國立中央大學
Abstract:	本篇論文研究圖形之分解(decompositions of graphs)與圖形之反魔標號(antimagic labelings of graphs)。在第一章，我們介紹一些術語跟需要的符號。第二~四章我們探討圖形之分解，第五章我們探討反魔圖。在第二章，我們將完全圖(the complete graphs)分解成兩種特別的圖形，兩種圖邊的個數在考慮之內。在第三章，我們討論λ重邊完全圖的最大的(Pk,Sk)-填充與最小的(Pk,Sk)-覆蓋及最大的(Pk,Ck)-填充與最小的(Pk,Ck)-覆蓋。在第四章，我們證得蜘蛛圖(spiders)分解成t個同構的圖形的充份必要條件。在第五章，我們得到星林圖(star forest)是反魔圖的一個必要條件和一個充份條件，且得到mS2∪Sn是反魔圖的充份必要條件。;In this thesis, we investigate decompositions and antimagic labelings of graphs. In Chapter 1, we give some terminology and notation needed in the thesis. Chapter 2∼4 concern decompositions of graphs. Chapter 5 concerns antimagic labelings of graphs. In Chapter 2, we consider the problems about decompositions of the complete graphs Kn into two kinds of graphs, each with specific numbers of edges. In Chapter 3, the problems of the maximum (Pk; Sk)-packing, the minimum (Pk; Sk)- covering, the maximum (Ck; Sk)-packing and the minimum (Ck; Sk)-covering of Kn are investigated. In Chapter 4, we give necessary and sufficient conditions for the spiders to be t- decomposable. In Chapter 5, we obtain a necessary condition for the star forest to be antimagic and a sufficient condition for the star forest to be antimagic, and necessary and sufficient conditions for mS2 ∪ Sn to be antimagic.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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