Neutrosophic Graphs Research Articles

A neutrosophic folding and retraction on a single-valued neutrosophic graph

The main aim of this article is to present neutrosophic folding and neutrosophic retractions on a single-valued neutrosophic graph Ğ from the viewpoint of geometry and topology. For this reason, we use a sequence of neutrosophic transformations on Ğ to obtain a new single-valued neutrosophic graph G ˇ 1 which contains different parameters under new conditions. We deduce the isometric neutrosophic folding on neutrosophic spheres and neutrosophic torii. Also, we determine the relationship between the limit neutrosophic folding and the limit of neutrosophic retraction on Ğ. Theorems regulating these relations are attained.

A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

Study on neutrosophic graph with application in wireless network

A neutrosophic network is an extension of an intuitionistic fuzzy network that provides more precision compatibility and flexibility than an intuitionistic fuzzy graph in structuring and modelling many real-life problems. The authors have explored the use of a neutrosophic network for modelling the passive optical network, mobile ad hoc network (MANET), and wireless sensor graph. They have presented the idea of strong arc, weak arc strong domination numbers, and strong perfect domination of neutrosophic network. They have described the method to find the values of strong and strong perfect domination of neutrosophic network. Finally, they use the idea of a strong arc strong domination number in MANET and wireless sensor graphs.

Study on single‐valued neutrosophic graph with application in shortest path problem

Study on single‐valued neutrosophic graph with application in shortest path problem

Dominating Energy in Neutrosophic graphs

Dominating Energy in Neutrosophic graphs

Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm

The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms.

A study on generalized graphs representations of complex neutrosophic information

A complex neutrosophic set is a useful model to properly handle incomplete information of periodic nature. This is characterized by three complex-valued components: truth, indeterminacy and falsity membership functions, whose range is extended from [0, 1] to unit circle in the complex plane. In this article, we define the notion of generalized complex neutrosophic graphs of type 1 and discuss certain of their properties, including regularity and completeness. Further, we describe these properties by several examples and present some of their interesting results. Moreover, we define the score function and accuracy function of complex neutrosophic sets. We describe decision making analysis based on generalized complex neutrosophic graphs of type 1. Finally, we highlight the significance of our proposed model by comparative analysis with the already existing models.

Pragmatic results in Taiwan education system based IVFG & IVNG

An interval-valued fuzzy graph (IVFG) and degree of vertices have been applied for performance evaluation in an educational system. The approach is mainly developed based on real membership values of vertices of an IVFG. In this manuscript, some definitions of generalized fuzzy graphs and neutrosophic graphs structures are improved. First, we have concentrated to improve the existing definitions for union and join of two IVFG’s, complete IVFG with supporting examples. Then, their modified version is developed. Secondly, the modified version of interval-valued neutrosophic graph (IVNG) is given. Third, an algorithm and a flowchart of the proposed method are described. Fourth, the generalized form of complete and strong IVNG is given with examples. Finally, a real-life application using interval-valued fuzzy graph in education system in Taiwan is exhibited.

A Study on Discrete Mathematics: Sum Distance in Neutrosophic Graphs with Application

A Study on Discrete Mathematics: Sum Distance in Neutrosophic Graphs with Application

A study of m-polar neutrosophic graph with applications

A study of m-polar neutrosophic graph with applications

Application of neutrosophic minimum spanning tree in electrical power distribution network

The problem of finding the minimum spanning tree (MST) is one of the most studied and important combinatorial optimisation problems in graph theory. Several types of uncertainties exist in real-life problems, which make it very hard to find the exact length of the arc. The neutrosophic set is an efficient tool to model and deal with the uncertainties in information due to inconsistent and indeterminate. In this study, the authors use triangular neutrosophic numbers to represent the edge weights of a neutrosophic graph for the MST problem in the neutrosophic environment. They call this problem a neutrosophic MST (NMST) problem. They formulate the NMST problem in terms of the linear programming model. Here, they introduce an algorithmic method based on a genetic algorithm for solving the NMST problem. They present the utility of triangular neutrosophic numbers as edge weights and their application in the electrical distribution network.

A Study on Bipolar Single-Valued Neutrosophic Graphs With Novel Application

A Study on Bipolar Single-Valued Neutrosophic Graphs With Novel Application

Neutrosophic Vague Incidence Graph

Vague sets gives more intuitive graphical notation of vague data, that devotes better analysis in information relationships, incompleteness and similarity measures. Neutrosophic graphs are used as a mathematical tool to kept an imprecise and unspecified information. In this paper, the neutrosophic vague incidence graphs are introduced. The edge-connectivity, vertex-connectivity and pair-connectivity in neutrosophic vague incidence graphs are established. The given results are illustrated with suitable example.

Representation of competitions by complex neutrosophic information

The concept of generalized complex neutrosophic graph of type 1 is an extended approach of generalized neutrosophic graph of type 1. It is an effective model to handle inconsistent information of periodic nature. In this research article, we discuss certain notions, including isomorphism, competition graph, minimal graph and competition number corresponding to generalized complex neutrosophic graphs. Further, we describe these concepts by several examples and present some of their properties. Moreover, we analyze that a competition graph corresponding to a generalized complex neutrosophic graph can be represented by an adjacency matrix with suitable real life examples. Also, we enumerate the utility of generalized complex neutrosophic competition graphs for computing the strength of competition between the objects. Finally, we highlight the significance of our proposed model by comparative analysis with the already existing models.

Dominating Energy in Neutrosophic graphs

Dominating energy of graphs plays a vital role in the field of application in energy. Results by applying neutrosophic graph theory is more efficient than other existing methods. So, dominating energy of neutrosophic graphs will also give more accurate results than other exixting methods in the field of energy. This article introduces dominating energy of neutrosophic graphs. Dominating energy of a neutrosophic graph, dominating neutrosophic adjacency matrix, eigen values for the dominating energy of a neutrosophic graphs and complement of neutrosophic graphs are defined with examples. Also, dominating energy in union and join operations of neutrosophic graphs are developed and some theorems in dominating energy of a neutrosophic graphs are derived here.

Research on the Shortest Path Solution Method of Interval Valued Neutrosophic Graphs Based on the Ant Colony Algorithm

The shortest path problem (SPP) is considerably important in several fields. After typhoons, the resulting damage leads to uncertainty regarding the path weight that can be expressed accurately. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership degrees of the elements. In an uncertain environment, neutrosophic numbers can express the edge distance more effectively. Based on the theories of interval valued neutrosophy and neutrosophic graphs, this paper proposes a shortest path solution method of interval valued neutrosophic graphs using the ant colony algorithm. Further, an analysis comparing the proposed algorithm with the Dijkstra algorithm was used to probe the potential shortcomings and advantages of the proposed method. In addition, this approach confirmed the effectiveness of the proposed algorithm. Furthermore, we investigated the convergence processes of the ant colony algorithm with different parameter settings, analyzed their results, and used different score functions to solve the SPP and analyze the results.

Link Prediction in Social Networks by Neutrosophic Graph

The computation of link prediction is one of the most important tasks on a social network. Several methods are available in the literature to predict links in networks and RSM index is one of them. The RSM index is applicable in the fuzzy environment and it does not incorporate the notion of falsity and indecency parameters which occur frequently in uncertain environments. In the present method, the behaviors of the common neighbor and the other parameters, like nature of job, location, etc., are considered. In this paper, more parameters are included in the RSM index for making it more flexible and realistic and it is best fitted in the neutrosophic environment. Many important properties are studied for this modified RSM index. A small network from Facebook is considered to illustrate the problem.

A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

In most realistic situations, the theory and method of multi-attribute decision-making have been widely used in different fields, such as engineering, economy, management, military, and others. Although many studies in some extended fuzzy contexts have been explored with multi-attribute decision-making, it is widely recognized that single-valued neutrosophic sets can describe incomplete, indeterminate and inconsistent information more easier. In this paper, aiming at addressing multi-attribute decision-making problems with single-valued neutrosophic information, related models and multi-attribute decision-making approaches based on the fuzzy graph theory are studied. In specific, the notion of single-valued neutrosophic sets and graphs is firstly introduced together with several common operational laws. Then a multi-attribute decision making method based on single-valued neutrosophic graphs is established. Finally, an illustrative example and a comparative analysis are conducted to verify the feasibility and efficiency of the proposed method.

Derivable Single Valued Neutrosophic Graphs Based on KM-Fuzzy Metric

In this paper we consider the concept of $KM$ -fuzzy metric spaces and we introduce a novel concept of $KM$ -single valued neutrosophic metric graphs based on $KM$ -fuzzy metric spaces. Then we investigate the finite $KM$ -fuzzy metric spaces with respect to $KM$ -fuzzy metrics and we construct the $KM$ -fuzzy metric spaces on any given non-empty sets. We try to extend the concept of $KM$ -fuzzy metric spaces to a larger class of $KM$ -fuzzy metric spaces such as union and product of $KM$ -fuzzy metric spaces and in this regard we investigate the class of products of $KM$ -single valued neutrosophic metric graphs. In the final, we define some operations such as tensor product, Cartesian product, semi-strong product, strong product, union, semi-ring sum, suspension, and complement of $KM$ -single valued neutrosophic metric graphs.

The Special Neutrosophic Functions

In this study, we introduce the notion of special neutrosophic functions as new kinds of neutrosophic function defined in a neutrosophic logic. As particular cases, we present the notions of neutrosophic Floor (greatest integer), neutrosophic Absolute Function and neutrosophic Signum Function. Moreover, we draw its neutrosophic graph representation and discuss similarities and differences for these special neutrosophic functions between the classic case and neutrosophic case. We investigate some properties and prove them. However, we often need the definition of absolute value function, especially in the metric space. Therefore, we introduce its initial definition in this study.