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Full-Text Articles in Discrete Mathematics and Combinatorics
Independent Domination In Complementary Prisms., Joel Agustin Gongora
Independent Domination In Complementary Prisms., Joel Agustin Gongora
Electronic Theses and Dissertations
Let G be a graph and G̅ be the complement of G. The complementary prism GG̅ of G 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. For example, if G is a 5-cycle, then GG̅ is the Petersen graph. In this paper we investigate independent domination in complementary prisms.
Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux
Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux
Electronic Theses and Dissertations
In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or …
Double Domination Of Complementary Prisms., Lamont D. Vaughan
Double Domination Of Complementary Prisms., Lamont D. Vaughan
Electronic Theses and Dissertations
The complementary prism of a graph G is obtained from a copy of G and its complement G̅ by adding a perfect matching between the corresponding vertices of G and G̅. For any graph G, a set D ⊆ V (G) is a double dominating set (DDS) if that set dominates every vertex of G twice. The double domination number, denoted γ×2(G), is the cardinality of a minimum double dominating set of G. We have proven results on graphs of small order, specific families and lower bounds on γ×2 …