Bipolar Neutrosophic Cubic Graphs and Its Applications

Bipolar Neutrosophic Cubic Graphs and Its Applications

C. Antony Crispin Sweety (Nirmala College for Women, India), K. Vaiyomathi (Nirmala College for Women, India) and F. Nirmala Irudayam (Nirmala College for Women, India)
DOI: 10.4018/978-1-5225-9380-5.ch021

Abstract

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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Background

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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