Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

5-2009

Committee Chair or Co-Chairs

Teresa W. Haynes

Committee Members

Robert A. Beeler, Debra J. Knisley

Abstract

Let G = (V (G), E(G)) be a graph and be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and by adding the edges of a perfect matching between the corresponding vertices of G and . A set DV (G) is a locating-dominating set of G if for every uV (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N(v)⋂D for all vV (G)D where vu. 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.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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