Degree Sequences and Statuses in Graphs

• Main Authors: Wei-han Tsai, 才維翰
• Other Authors: Chiang Lin
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/19584527171783016935

博士 === 國立中央大學 === 數學研究所 === 100 === 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