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

Copyright

Copyright by the authors.

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