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Domination in Fuzzy Graphs

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Fuzzy Graph Theory with Applications to Human Trafficking

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 365))

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Abstract

The results of the next two sections are based on Somasundaram, Somasundaram (Pattern Recongit Lett 19:787–791, 1998), [29]. The formal mathematical definition of domination was given by Ore, (Theory of graphs. American Mathematical Society, Providence, 1962), [22]. Cockayne and Hedetnieme, (Networks 7:247–261, 1977, [3]), published a survey paper on this topic in 1977 and since then hundreds of papers have been published on this subject. According to Somasundaram, Somasundaram (Pattern Recongit Lett 19:787–791, 1998, [29]), the rapid growth of research in this area is due to the following three factors. (1) The diversity of applications of domination theory to both real world and mathematical coverings or location problems. (2) The wide variety of domination parameters that can be defined. (3) The NP-completeness of the basic domination problem, its close and natural relationship to other NP-complete problems and the subsequent interest in finding polynomial time solutions to domination problems in special classes of graphs.

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Authors and Affiliations

  1. Department of Mathematics, Creighton University, Omaha, NE, USA

    John N. Mordeson & Davender S. Malik

  2. Department of Mathematics, National Institute of Technology, Calicut, Kerala, India

    Sunil Mathew

Authors
  1. John N. Mordeson
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  2. Sunil Mathew
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  3. Davender S. Malik
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Correspondence to John N. Mordeson .

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Mordeson, J.N., Mathew, S., Malik, D.S. (2018). Domination in Fuzzy Graphs. In: Fuzzy Graph Theory with Applications to Human Trafficking. Studies in Fuzziness and Soft Computing, vol 365. Springer, Cham. https://doi.org/10.1007/978-3-319-76454-2_2

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  • DOI: https://doi.org/10.1007/978-3-319-76454-2_2

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