#### Date of Award

12-1-2016

#### Degree Name

Master of Science

#### Department

Mathematics

#### First Advisor

McSorley, John

#### Abstract

A Spanning tree of a graph G is a subgraph that is a tree which concludes all of the vertices of G. And a graph G is bipartite if the vertex set of G can be partitioned in to two sets A and B, such that every edge of G joins a vertex of A and a vertex of B. We can see that every tree(including spanning tree) is bipartite. We define type of a spanning tree using this idea as follows: We divide vertices of a spanning trees in to two partitions A and B by using its bipartition. Then, we define type of the spanning tree by (| A |, | B |), provided | A | less than or equal to | B |. We first identify the characteristics for a graph to have a spanning trees of a certain type. Then, implement some theorems about the type.

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