#### Term of Award

Summer 2018

#### Degree Name

Master of Science in Mathematics (M.S.)

#### Document Type and Release Option

Thesis (open access)

#### Copyright Statement / License for Reuse

This work is licensed under a Creative Commons Attribution 4.0 License.

#### Department

Department of Mathematical Sciences

#### Committee Chair

Hua Wang

#### Committee Member 1

Daniel Grey

#### Committee Member 2

Jie Zhang

#### Abstract

In this thesis, we consider the properties of sparse trees and summarized a certain class of trees under some constraint (including with a given degree sequence, with given number of leaves, with given maximum degree, etc.) which have maximum Wiener index and the minimum number of subtrees at the same time. Wiener index is one of the most important topological indices in chemical graph theory. Steiner k Wiener index can be regarded as the generalization of Wiener index, when k = 2, Steiner Wiener index is the same as Wiener index. Steiner k Wiener index of a tree T is the summation of all sizes of subtrees which contain any ksubset of vertex set V (T). In sparse trees with a given degree sequence, by using a computer, we give some computational results with regarding to Steiner Wiener index, which may shed light on the extremal tree with maximum Steiner Wiener index.

#### Recommended Citation

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#### Research Data and Supplementary Material

No