Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

12-2008

Committee Chair or Co-Chairs

Teresa W. Haynes

Committee Members

Debra J. Knisley, Robert B. Gardner

Abstract

In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or bipartite, and we will obtain bounds on the chromatic number of a complementary prism. We will finish the thesis with a section on possible future problems.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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