Domination and total domination in complementary prisms |
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Authors: | Teresa W Haynes Michael A Henning Lucas C van der Merwe |
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Institution: | (1) Department of Mathematics, East Tennessee State University, Johnson City, TN 37614-0002, USA;(2) School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209, South Africa;(3) Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA |
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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.
Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal. |
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Keywords: | Cartesian product Complementary prism Domination Total domination |
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