Restrained and Other Domination Parameters in Complementary Prisms.

<p>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 <em>distance</em> - <em>k</em> 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.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - unrestricted

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.issued

2008

Author dc:creator

• DesOrmeaux, Wyatt Jules

• chromatic number
• complementary prism
• graph theory
• stratification
• distance-k domination
• 2-step domination
• restrained domination
• Discrete Mathematics and Combinatorics
• Mathematics
• Physical Sciences and Mathematics

Statement dc:rights

• Copyright by the authors.

Repository record dc:identifier

https://dc.etsu.edu/etd/1998

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-3350