Fractional dominations and fractional total dominations of graph complements (Q1613430)
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scientific article; zbMATH DE number 1792367
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fractional dominations and fractional total dominations of graph complements |
scientific article; zbMATH DE number 1792367 |
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Fractional dominations and fractional total dominations of graph complements (English)
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29 August 2002
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Let \(\gamma_f(G)\) and \(\Gamma_f(G)\) be the fractional domination number and the fractional total domination number of a graph \(G\). If \(\overline G\) is the complement of \(G\), then the main result says that \({\gamma_f(G)}^{-1}+ {\Gamma_f(\overline G)}^{-1}=1.\) As an application of this identity, the author presents results for these parameters on the join of graphs, Mycielski's construction, and some graph products.
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fractional total domination
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graph complement
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