圖形之分割與反魔標號

Decompositions and Antimagic Labelings of Graphs

陳抮君(Zhen-Chun Chen)

指導教授 ： 林強

國立中央大學/理學院/數學系/博士(2015年)

摘要

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。

關鍵字

圖形之分割 ； 反魔標號

並列摘要

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.

並列關鍵字

decompositions ； antimagic

參考文獻

[1] A. Abueida, S. Clark, and D. Leach, Multidecomposition of the complete graph into graph

[3] A. Abueida and M. Daven,Multidecompositions of several graph products, Graphs Combin.

29 (2013), 315–326.

[4] A. Abueida and M. Daven, Multidesigns for graph-pairs of order 4 and 5, Graphs Combin.

[5] B. Alspach, D. Dyes and D. L. Kreher, On isomorphic factorization of circulant graphs,