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Inequality of Nordhaus-Gaddum type for total outer-connected domination in graphs
Authors:Hong Xing Jiang  Li Ying Kang
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
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.
Keywords:Graph  domination number  total outer-connected domination  Nordhaus-Gaddum inequality
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