Bipolar Neutrosophic Cubic Graphs and Its Applications

Bipolar Neutrosophic Cubic Graphs and Its Applications

C. Antony Crispin Sweety, K. Vaiyomathi, F. Nirmala Irudayam
DOI: 10.4018/978-1-5225-9380-5.ch021
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The authors introduce neutrosophic cubic graphs and single-valued netrosophic Cubic graphs in bipolar setting and discuss some of their algebraic properties such as Cartesian product, composition, m-union, n-union, m-join, n-join. They also present a real time application of the defined model which depicts the main advantage of the same. Finally, the authors define a score function and present minimum spanning tree algorithm of an undirected bipolar single valued neutrosophic cubic graph with a numerical example.
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L. Zadeh (1965) introduced the concept of fuzzy sets by defining the degree of membership to deal with the data with uncertainties. To cope with the lack of non-membership degree K. T. Atanossov (1986) proposed the notion of intuitionistic fuzzy sets by associating the degree of non-membership in the concept of fuzzy set as an individual element. In addition to this Gau W. L and Buehrer D. J (1993) introduced vague sets. F. Smarandache (1999) introduced neutrosophic logic to handle and understand the indefinite information in a more effective way. F. Smaradache (2006) introduced neutrosophic sets as a generalization intuitionistic Fuzzy sets. Every element of a neutrosophic element has three grades of membership defined within the real non-standard interval ]–0, 1+[. H. Wang and F. Smarandache (2010) defined single valued neutrosophic set which is a subclass of neutrosophic sets with three membership functions that are independent and their value defined in [0,1].

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