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- W4285261572 abstract "A set (S) of vertices in an isolate-free graph (G) is a total dominating set if every vertex in (G) is adjacent to a vertex in (S). A total dominating set of (G) is minimal if it contains no total dominating set of (G) as a proper subset. The upper total domination number (Gamma_t(G)) of (G) is the maximum cardinality of a minimal total dominating set in (G). We establish Nordhaus-Gaddum bounds involving the upper total domination numbers of a graph (G) and its complement (overline{G}). We prove that if (G) is a graph of order (n) such that both (G) and (overline{G}) are isolate-free, then (Gamma_t(G) + Gamma_t(overline{G}) leq n + 2) and (Gamma_t(G)Gamma_t(overline{G}) leq frac{1}{4}(n+2)^2), and these bounds are tight." @default.
- W4285261572 created "2022-07-14" @default.
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- W4285261572 date "2022-01-01" @default.
- W4285261572 modified "2023-09-30" @default.
- W4285261572 title "Nordhaus-Gaddum bounds for upper total domination" @default.
- W4285261572 doi "https://doi.org/10.7494/opmath.2022.42.4.573" @default.
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