#### Defense Date

2011

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Department

Mathematical Sciences

#### First Advisor

Craig Larson

#### Abstract

In the 1970's computer scientists developed the theory of computational complexity. Some problems seemed hard-to-compute, while others were easy. It turned out that many of the hard problems were equally hard in a way that could be precisely specified. They became known as the NP-complete problems. The SATISFIABILITY problem (SAT) was the first problem to be proved NP-complete in 1971. Since then numerous other hard-to-solve problems have been proved to be in NP-complete. In this paper we will examine the problem of how to find a maximum independent set of vertices for a graph. This problem is known as Maximum Independent Set (MIS) for a graph. The corresponding decision problem for MIS is the question, given an integer K, is there a independent set with at least K vertices? This decision problem is INDEPENDENT SET (IS). The intention of this paper is to show through polynomial transformation that IS is in the set of NP-complete Problems. We intend to show that 3SAT is NP-complete and then using this fact, that IS is NP-complete.

#### Rights

© The Author

#### Is Part Of

VCU University Archives

#### Is Part Of

VCU Theses and Dissertations

#### Date of Submission

September 2011