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Symmetry 2018, 10(6), 203; https://doi.org/10.3390/sym10060203

A Study on Neutrosophic Cubic Graphs with Real Life Applications in Industries

1
Department of Mathematics, Hazara University, Mansehra 21120, Pakistan
2
Department of Mathematics, College of Science, Majmaah University, Al-Zulfi 11952, Saudi Arabia
3
Department of Mathematics, University of New Mexico, Albuquerque, NM 87301, USA
*
Author to whom correspondence should be addressed.
Received: 27 April 2018 / Revised: 29 May 2018 / Accepted: 30 May 2018 / Published: 5 June 2018
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Abstract

Neutrosophic cubic sets are the more generalized tool by which one can handle imprecise information in a more effective way as compared to fuzzy sets and all other versions of fuzzy sets. Neutrosophic cubic sets have the more flexibility, precision and compatibility to the system as compared to previous existing fuzzy models. On the other hand the graphs represent a problem physically in the form of diagrams, matrices etc. which is very easy to understand and handle. So the authors applied the Neutrosophic cubic sets to graph theory in order to develop a more general approach where they can model imprecise information through graphs. We develop this model by introducing the idea of neutrosophic cubic graphs and introduce many fundamental binary operations like cartesian product, composition, union, join of neutrosophic cubic graphs, degree and order of neutrosophic cubic graphs and some results related with neutrosophic cubic graphs. One of very important futures of two neutrosophic cubic sets is the R-union that R-union of two neutrosophic cubic sets is again a neutrosophic cubic set, but here in our case we observe that R-union of two neutrosophic cubic graphs need not be a neutrosophic cubic graph. Since the purpose of this new model is to capture the uncertainty, so we provide applications in industries to test the applicability of our defined model based on present time and future prediction which is the main advantage of neutrosophic cubic sets. View Full-Text
Keywords: neutrosophic cubic set; neutrosophic cubic graphs; applications of neutrosophic cubic graphs neutrosophic cubic set; neutrosophic cubic graphs; applications of neutrosophic cubic graphs
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Gulistan, M.; Yaqoob, N.; Rashid, Z.; Smarandache, F.; Wahab, H.A. A Study on Neutrosophic Cubic Graphs with Real Life Applications in Industries. Symmetry 2018, 10, 203.

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