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 of Mathematical Sciences

Committee Chair

Hua Wang

Committee Member 1

Colton Magnant

Committee Member 2

Andrew Sills


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.