Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Gary Chartrand

Second Advisor

S. F. Kapoor

Third Advisor

Arthur White

Fourth Advisor

Kenneth Williams


One of the major areas in Graph Theory is domination in graphs. It is this area with which this dissertation deals, with the primary emphasis on step domination in graphs.

In Chapter 1 we present some preliminary definitions and examples. In addition, a background of the area of domination is presented. We then introduce the concepts that lead to step domination.

In Chapter II we formally define the concept of step domination and give several examples. We determine the minimum number of vertices needed in a step domination set for many classes of graphs. We then explore step domination for trees. Finally, we define a new graph to help in our investigation of step domination.

For some graphs a step domination set must consist of the entire vertex set. In Chapter III we discuss situations when this happens. We also discuss various interpretations of uniqueness for step domination sets.

Many variations of step domination exist In Chapter IV we introduce a number of these variations and discuss properties of each.


Fifth Advisor: Joseph Buckley

Access Setting

Dissertation-Open Access