Extremal Graph Theory and Enumerative Combinatorics

<p>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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (restricted to Georgia Southern)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Yuan, Shuai

Contributors dc:contributor

• Colton Magnant
• Andrew Sills

• ETD
• Center
• Centroid
• Subtree Core
• S-Order
• Spectral Moment
• Discrete Mathematics and Combinatorics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1133

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2177