Domination and Total Domination in Complementary Prisms
Document Type
Article
Publication Date
7-1-2009
Description
Let G be a graph and Ḡ be the complement of G. The complementary prism GḠ of G is the graph formed from the disjoint union of G and Ḡ by adding the edges of a perfect matching between the corresponding vertices of G and Ḡ. For example, if G is a 5-cycle, then GḠ is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, max {γ(G), γ(Ḡ)} ≤ γ (Ḡ)and max {γt(G), γt(Ḡ)} ≤ γt (Gγ), where γ(G) and γt(G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.
Citation Information
Haynes, Teresa W.; Henning, Michael A.; and Van Der Merwe, Lucas C.. 2009. Domination and Total Domination in Complementary Prisms. Journal of Combinatorial Optimization. Vol.18(1). 23-37. https://doi.org/10.1007/s10878-007-9135-8 ISSN: 1382-6905