Domination and total domination in complementary prisms
TW Haynes, MA Henning… - Journal of Combinatorial …, 2009 - Springer
TW Haynes, MA Henning, LC Van Der Merwe
Journal of Combinatorial Optimization, 2009•SpringerLet G be a graph and G be the complement of G. The complementary prism GG of G is the
graph formed from the disjoint union of G and G by adding the edges of a perfect matching
between the corresponding vertices of G and G. For example, if G is a 5-cycle, then GG 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(G)\}≤γ(GG) and
\max{t(G),t(G)\}≤t(GG), where γ (G) and γ t (G) denote the domination and total domination …
graph formed from the disjoint union of G and G by adding the edges of a perfect matching
between the corresponding vertices of G and G. For example, if G is a 5-cycle, then GG 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(G)\}≤γ(GG) and
\max{t(G),t(G)\}≤t(GG), where γ (G) and γ t (G) denote the domination and total domination …
Abstract
Let G be a graph and be the complement of G. The complementary prism of G 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 . For example, if G is a 5-cycle, then is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, and , where γ(G) and γ t (G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.
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