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

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/53203

Title:	圖的程度序列和狀態;Degree Sequences and Statuses in Graphs
Authors:	才維翰;Wei-han Tsai
Contributors:	數學研究所
Keywords:	程度序列;狀態;degree sequence;status
Date:	2012-01-16
Issue Date:	2012-06-15 20:27:52 (UTC+8)
Abstract:	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。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
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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