New concepts in neutrosophic graphs with application

Akram, Muhammad; Siddique, Saba; Davvaz, Bijan

doi:10.1007/s12190-017-1106-3

Cited by 14 publications

(2 citation statements)

References 15 publications

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“…An important feature of this book is that it contains over 200 neutrosophic graphs to provide better understandings of these concepts. Akram and others discussed different aspects of neutrosophic graphs [30][31][32][33]. Further Jun et al [34] gave the idea of cubic set and it was characterized by interval valued fuzzy set and fuzzy set, which is more general tool to capture uncertainty and vagueness, while fuzzy set deals with single value membership and interval valued fuzzy set ranges the membership in the form of interval.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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“…The membership function of the fuzzy edge set is employed by Rosenfeld [38] to describe whether two vertices were joined by an edge or not. There are some new concepts related to fuzzy phenomena in graph theory, such as: bipolar fuzzy graphs [2], intuitionistic fuzzy hypergraphs [6], strong intuitionistic fuzzy graphs [5], Nhypergraphs [4], fuzzy soft graphs [8], bipolar fuzzy digraphs [3], regular interval-valued fuzzy graphs [41], generalized fuzzy hypergraphs [17], domination in mpolar fuzzy graphs [9], and neutrosophic graphs [10]. Furthermore, the fuzzy phenomena in graph coloring problem has been investigated by Rosyida et al [39] which developed a method to determine a fuzzy chromatic number of fuzzy graph.…”

Section: Introductionmentioning

confidence: 99%

Cycle index of uncertain random graph

Chen

Peng

Rao

et al. 2018

IFS

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Abstract. With the increasing of the complexity of a system, there is a variety of indeterminacy in the practical applications of graph theory. We focus on uncertain random graph, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. In this paper, the chance theory is applied to construct the cycle index of an uncertain random graph. Then a method to calculate the cycle index of an uncertain random graph is presented. We also discuss some properties of the cycle index.

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