## Theses and Dissertations

#### Title

Bounds for the independence number of a graph

2011

Thesis

#### Degree Name

Master of Science

#### Department

Mathematical Sciences

Craig Larson

#### Abstract

The independence number of a graph is the maximum number of vertices from the vertex set of the graph such that no two vertices are adjacent. We systematically examine a collection of upper bounds for the independence number to determine graphs for which each upper bound is better than any other upper bound considered. A similar investigation follows for lower bounds. In several instances a graph cannot be found. We also include graphs for which no bound equals $\alpha$ and bounds which do not apply to general graphs.

#### Is Part Of

VCU University Archives

#### Is Part Of

VCU Theses and Dissertations

September 2011

COinS