#### Date of Defense

4-19-1994

#### Department

Mathematics

#### First Advisor

Arthur T. White, Mathematics & Statistics

#### Second Advisor

Gary Chartrand, Mathematics & Statistics

#### Third Advisor

Elise deDonker

#### Abstract

In recent years, there has been interest in the mathematical community in a rapidly developing branch of theoretical mathematics known as random topological graph theory. This new area of mathematics explores the different ways in which certain graphs can be imbedded in given surfaces. The random nature of the new branch results when one also imposes a random distribution on set of all imbeddings of a fixed graph, via the orientation of the edges at each vertex. Using the technique of J. Edmonds, developed in 1960, this paper explores the imbeddings for the graph Q_{3} using a particular group and a particular generating set.

#### Recommended Citation

Koenemann, Jody, "Average Genus of the Cube" (1994). *Honors Theses*. 281.

http://scholarworks.wmich.edu/honors_theses/281

#### Access Setting

Honors Thesis-Open Access