Term of Award
Summer 2014
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (restricted to Georgia Southern)
Department
Department of Mathematical Sciences
Committee Chair
Hua Wang
Committee Member 1
Colton Magnant
Committee Member 2
Andrew Sills
Abstract
This thesis consists of research on two topics.The first topic is about different middle parts of trees, such as center, centroid, subtree core. In this work, we considered how far apart (with given order of the tree) two different `middle points' can be and when such maximum distances are achieved. We also naturally extended to trees with restricted degrees or diameter. The second topic is about trees with given degree sequence in S-order. The first trees in S-order with the additional condition that the nonleaf vertex degrees are different from each other are characterized by making use of the interpretation of the spectral moment in terms of numbers of paths and the product of adjacent vertex degrees.
Recommended Citation
Yuan, Shuai, "Extremal Graph Theory and Enumerative Combinatorics" (2014). Electronic Theses and Dissertations. 1133.
https://digitalcommons.georgiasouthern.edu/etd/1133
