#### Degree Name

MS (Master of Science)

#### Program

Mathematical Sciences

#### Date of Award

12-2012

#### Committee Chair or Co-Chairs

Teresa W. Haynes

#### Committee Members

Debra J. Knisley, Robert A. Beeler

#### Abstract

A set *S* of vertices in a graph *G* = (*V*,*E*) is a dominating set if every vertex in *V* \ *S* is adjacent to at least one vertex in *S*. A vertex *v* in a dominating set *S* is said to be it *cost effective* if it is adjacent to at least as many vertices in *V* \ *S* as it is in *S*. A dominating set S is cost effective if every vertex in S is cost effective. The minimum cardinality of a cost effective dominating set of *G* is the cost effective domination number of G. In addition to some preliminary results for general graphs, we give lower and upper bounds on the cost effective domination number of trees in terms of their domination number and characterize the trees that achieve the upper bound. We show that every value of the cost effective domination number between these bounds is realizable.

#### Document Type

Thesis - Open Access

#### Recommended Citation

McCoy, Tabitha Lynn, "Cost Effective Domination in Graphs" (2012). *Electronic Theses and Dissertations.* Paper 1485. http://dc.etsu.edu/etd/1485

#### Copyright

Copyright by the authors.