MS (Master of Science)
Date of Award
Committee Chair or Co-Chairs
Teresa W. Haynes
Robert A. Beeler, Debra J. Knisley
Let G = (V (G), E(G)) be a graph and G̅ be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. A set D ⊆ V (G) is a locating-dominating set of G if for every u ∈ V (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N(v)⋂D for all v ∈ V (G)D where v ≠ u. The locating-domination number of G is the minimum cardinality of a locating-dominating set of G. In this thesis, we study the locating-domination number of complementary prisms. We determine the locating-domination number of GG̅ for specific graphs and characterize the complementary prisms with small locating-domination numbers. We also present bounds on the locating-domination numbers of complementary prisms.
Thesis - Open Access
Holmes, Kristin Renee Stone, "Locating-Domination in Complementary Prisms." (2009). Electronic Theses and Dissertations. Paper 1871. https://dc.etsu.edu/etd/1871
Copyright by the authors.