Locating-Domination in Complementary Prisms.

<p>Let <em>G</em> = (<em>V</em> (<em>G</em>), <em>E</em>(<em>G</em>)) be a graph and <em>G&#773;</em> be the complement of <em>G</em>. The complementary prism of <em>G</em>, denoted <em>GG&#773;</em>, is the graph formed from the disjoint union of <em>G</em> and <em>G&#773;</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em> and <em>G&#773;</em>. A set <em>D</em> &#8838; <em>V</em> (<em>G</em>) is a locating-dominating set of <em>G</em> if for every <em>u</em> &#8712; <em>V</em> (<em>G</em>)<em>D</em>, its neighborhood <em>N</em>(<em>u</em>)&#8898;<em>D</em> is nonempty and distinct from <em>N</em>(<em>v</em>)&#8898;<em>D</em> for all <em>v</em> &#8712; <em>V</em> (<em>G</em>)<em>D</em> where <em>v</em> &#8800; <em>u</em>. The locating-domination number of <em>G</em> is the minimum cardinality of a locating-dominating set of <em>G</em>. In this thesis, we study the locating-domination number of complementary prisms. We determine the locating-domination number of <em>GG&#773;</em> for specific graphs </em> and characterize the complementary prisms with small locating-domination numbers. We also present bounds on the locating-domination numbers of complementary prisms.</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

2009

Author dc:creator

• Holmes, Kristin Renee Stone

• Locating-Domination
• Complementary Prisims
• 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/1871

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-3223