圖的程度序列和狀態

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才維翰(Wei-han Tsai) 查詢紙本館藏

畢業系所

數學系

論文名稱

圖的程度序列和狀態
(Degree Sequences and Statuses in Graphs)

相關論文

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★ On n-good graphs	★ A Note On Degree-Continuous Graphs
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★ 圖形之分割與反魔標號

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摘要(中)

在我的博士論文裡面我考慮了一些有關 degree sequences 和 statuses問題。
在第二章裡面我在一些特殊的 families 找出哪些圖在那些我所指定的 family 是唯一的, 例如: trees, connected regular graphs, forests, unicyclic graphs 和 bicyclic graphs。
在第三章裡面我考慮的問題是如何將一個圖嵌入另一個圖之中﹐並且使的原本的圖是後來這個擴展的圖的median。
在第四章裡面我先介紹了一個圖的變化光譜的定義。並且找出某幾類的圖的變化光譜。另外﹐在點數跟maximum degree固定的情況下﹐我也找出了到底有哪些圖的 status 可以達到最小。

摘要(英)

In this thesis, we consider some problems about degree sequences and statuses
of graphs.
In Chapter 2 we obtain the graphs which are degree unique in trees, connected
regular graphs, forests, unicyclic graphs and bicyclic graphs, respectively.
In Chapter 3 we consider the problem of embedding a given graph as the
median of another graph. We investigate the problem in the weighted version
and for some related notions such as antimedian and i-th median (i = 1, 2, . . .).
In Chapter 4 we investigate the variance spectrums of graphs. We also
characterize the graphs whose minimum statuses attain the minimum in the
family of graphs with fixed maximum degree and order

關鍵字(中)

★ 程度序列
★ 狀態

關鍵字(英)

★ degree sequence
★ status

論文目次

Contents
1 Introduction 1
1.1 Basic Definitions and Notations . . . . . . . . . . . . . . . . . . 1
1.2 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 3
2 Degree Unique Graphs 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Degree Unique Graphs in Trees . . . . . . . . . . . . . . . . . . 7
2.3 Degree Unique Graphs in Unicyclic Graphs and Bicyclic Graphs 12
3 Embedding Results for Medians and Antimedians 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Embedding Results for Medians . . . . . . . . . . . . . . . . . . 25
3.3 Embedding Results for Medians and Antimedians . . . . . . . . 33
4 Minimum Statuses and Variance Spectrums 51
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Minimum Statuses . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Variance Spectrums . . . . . . . . . . . . . . . . . . . . . . . . . 65
References 69

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指導教授

林強(Chiang Lin)

審核日期

2012-1-16

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