Inequality of Nordhaus-Gaddum type for total outer-connected domination in graphs |
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Authors: | Hong Xing Jiang Li Ying Kang |
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Institution: | [1]College of Mathematics and Information Science, Wenzhou University, Wenzhou 325000, P. R. China [2]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China |
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Abstract: | A set S of vertices in a graph G = (V, E) without isolated vertices is a total outer-connected dominating set (TCDS) of G if S is a total dominating set of G and GV − S] is connected. The total outer-connected domination number of G, denoted by γ
tc
(G), is the minimum cardinality of a TCDS of G. For an arbitrary graph without isolated vertices, we obtain the upper and lower bounds on γ
tc
(G) + γ
tc
($
\bar G
$
\bar G
), and characterize the extremal graphs achieving these bounds. |
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Keywords: | Graph domination number total outer-connected domination Nordhaus-Gaddum inequality |
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