Domination in fuzzy graphs

John N. Mordeson, Sunil Mathew, Davender S. Malik

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.

Original languageEnglish (US)
Title of host publicationStudies in Fuzziness and Soft Computing
PublisherSpringer Verlag
Pages57-85
Number of pages29
DOIs
Publication statusPublished - Jan 1 2018

Publication series

NameStudies in Fuzziness and Soft Computing
Volume365
ISSN (Print)1434-9922

Cite this

Mordeson, J. N., Mathew, S., & Malik, D. S. (2018). Domination in fuzzy graphs. In Studies in Fuzziness and Soft Computing (pp. 57-85). (Studies in Fuzziness and Soft Computing; Vol. 365). Springer Verlag. https://doi.org/10.1007/978-3-319-76454-2_2