Cost Effective Domination in Graphs

<p>A set <em>S</em> of vertices in a graph <em>G</em> = (<em>V</em>,<em>E</em>) is a dominating set if every vertex in <em>V</em> \ <em>S</em> is adjacent to at least one vertex in <em>S</em>. A vertex <em>v</em> in a dominating set <em>S</em> is said to be it <em>cost effective</em> if it is adjacent to at least as many vertices in <em>V</em> \ <em>S</em> as it is in <em>S</em>. 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 <em>G</em> 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.</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

2012

Author dc:creator

• McCoy, Tabitha Lynn

• cost effective domination number
• cost effective 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/1485

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-2678