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
