Neutrosophic Graphs Research Articles

Antipodal Turiyam Neutrosophic Graphs

Graph theory, a mathematical field, investigates the relationships between entities through vertices and edges [29]. Within this discipline, Uncertain Graph Theory emerges to model uncertainties in realworld networks. This paper presents the concept of the Antipodal Turiyam Neutrosophic Graph. In an Antipodal Graph, two nodes are connected if their shortest path distance equals the graph's diameter, emphasizing connections between the farthest nodes. Turiyam Neutrosophic Graphs extend traditional graphs by introducing four membership values-truth, indeterminacy, falsity, and liberal state-assigned to each vertex and edge, enabling a more nuanced representation of complex relationships.

Study for General Plithogenic Soft Expert Graphs

Graph theory, a branch of mathematics, focuses on studying graphs that model relationships between objects through vertices and edges [29]. The Turiyam Neutrosophic Graph handles uncertainty by assigning four values to vertices and edges: truth, indeterminacy, falsity, and liberal state. In contrast, the Plithogenic Graph is a general structure where vertices and edges are defined by degrees of appurtenance and contradiction across multiple attributes [45]. The General Plithogenic Graph extends the Plithogenic Graph, offering a broader framework [45]. This study presents new concepts of the General Plithogenic Soft Expert Graph and the Turiyam Neutrosophic Soft Expert Graph, with the former expanding the existing Soft Expert Graph model into a more generalized structure.

Sensitivity analysis and application of single-valued neutrosophic transportaion problem

The neutrosophic set serves as a powerful tool for addressing complexity, ambiguity, and managing imperfect and inconsistent information in the digital world. Graph theory plays a crucial role in determining the shortest path for neutrosophic sets through graph algorithms. This article introduces a novel algorithm, the bipartite graph contraction algorithm, to elucidate the graphical aspects within neutrosophic set theory by using score function for ranking. The proposed bipartite neutrosophic graph contraction algorithm is applied to solve a single-valued neutrosophic network, where the transportation unit cost is expressed as a trapezoidal single-valued neutrosophic number and produced the result as 〈364,537,694,908;0.3,0.7,0.7〉. A comparative analysis with an existing algorithm is conducted, and a novel introduction of sensitivity analysis in the realm of neutrosophic set theory is presented to assess the optimality of the result in neutrosophic transportation problems.

Product Perspective from Fuzzy to Neutrosophic Graph Extension- A Review of Literature

This review article consolidates and tabulates research on the product operations done in fuzzy, intuitionistic fuzzy, and neutrosophic graphs. This article encompasses the previous product discussions on fuzzy graphs and their extensions. This article aims to list the origin, structural properties, applications, etc. done by the researchers and academicians using the product behavior of two graphs on the fuzzified environment. This review provides a clear understanding of enhancements of product approach on graphs from fuzzy to neutrosophic kind.

Site Selection for Thermal Power Plant Based on Sombor Index in Neutrosophic Graph

A graph or molecular graph’s overall resilience and connectedness are gauged by the Sombor Index (SOI). It is an improved version of the conventional SOI that is designed to capture ambiguity in the relationships between nodes or atoms. This indicator aids in assessing the network’s resilience and stability in erratic circumstances. We have investigated the charac-teristics of the SOI of neutrosophic graphs (N Gs) in this study. The association between the neutrosophic first Zagreb Index (N FZI) of N Gs and the neutrosophic Sombor Index (N SI) was revealed in the study. The application of SOI based on Site Selection for Thermal Power Plants in N Gs is finally covered.

Domination and paired domination in Turiyam graphs with application

A potent tool in the theory of graphs, the Neutrosophic graph, is used to describe the variety of real-world cases with uncertainty brought on by ambiguous, inconsistent, and unpredictable data. In order to handle unpredictability in data sets larger than the current true, false, and not exactly known zones, the Turiyam graph was recently introduced. In both theoretical and applied graph theory environments, the ideas of domination and paired domination are crucial. For this reason, the current study introduces the ideas of domination and paired domination in Turiyam graphs together with the characteristics of each concept. Furthermore, domination in complete bipartite graphs, strong paired domination, and the application of paired domination are all worked out.

Forgotten Topological Index and its Properties on Neutrosophic Graphs

Topological indices play a significant role in crisp, fuzzy graphs and their real-life application. But to avoid the vagueness in the final result, these indices should be dealt with in the neutrosophic environment since it consolidates the uncertain quantity or values of an event in the name of "indeterminacy membership". Except for the wiener index, no other indices are introduced under the neutrosophic graphical setting. In this article, we consider the forgotten topological index (ToI) and the Edge forgotten index in the 3-valued logic neutrosophic graph and came up with some important theorem results and applications.

Embedding of Neutrosophic Graphs on Topological Surfaces

Background: A planar graph (PG) is a graph with no intersecting edges. Particular to both crisp and neutrosophic graphs (NG) is the planar graph, in contrast to crisp planar graphs. NPGs allow for the intersection of neutrosophic edge NEs, since the value of planarity in these graphs is the degree of planarity of the intersected NEs. The NPGs are often represented on a flat surface. Materials and Methods: This study discusses how to embed NGs on surfaces such as spheres and m-toruses by defining the degree of intersection of the neutrosophic edges of NGs with finding the faces on the given graph structures using Euler's theorems. Here, the proofs of Euler's theorems help us find, given the total NFV of G, the interval containing that value. Result: As result of this work obtained that for any two isomorphic planer graphs, they have the same planarity value. For any neutrosophic planer graph with f = (1,1,1) can be embedded in the plane if it can be embedded in the sphere and according to NPGs, for planar and spherical surfaces, equivalent theorems to Euler's formula are proved and shown. Conclusion: It concludes that by using neutrosophic sets and crisp graphs to construct neutrosophic graphs with the benefit of Euler’s theorem, it can provide the concept of embedding neutrosophic graphs in different topological surfaces such as a plane, sphere, and m-torus.

Study on Neutrosophic Graph with Application on Earthquake Response Center in Japan

Study on Neutrosophic Graph with Application on Earthquake Response Center in Japan

A Novel Approach on Energy of λJ-dominating Single-Valued Neutrosophic Graph Structure

The concept of dominance is one of the most important ideas in graph theory for handling random events, and it has drawn the interest from many scholars. Research related to graph energy has garnered a lot focus recently. The application of single-valued neutrosophic graphs (SVNGs) for energy, Laplacian energy, and dominating energy has been recommended by previous studies. In this research, we apply the concepts of single-valued neutrosophic sets (SVNS) to graph structures (GSs) and investigate some intriguing features of single-valued neutrosophic graph structures (SVNGS). Moreover, the notions of λJ-dominating energy GS in an SVNGS environment are analyzed in this study. More specifically, illustrative examples are used to develop the adjacency matrix of a λJ-dominating SVNGS, as well as the spectrum of the adjacency matrix and their related theory. Further, the SVNGS λJ-dominating energy is determined. We go over various characteristics and constraints for the energy of SVNGS with λJ-dominating. Further, we introduce the idea of isomorphic and identical λJ-dominating SVNGS energy, which has been studied using relevant examples, and some of its established properties are presented.

Theory and Application of Interval-Valued Neutrosophic Line Graphs

Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is crucial to represent the problems. Line graphs of neutrosophic graphs are significant due to their ability to represent and analyze uncertain or indeterminate information about edge relationships and complex networks in graphs. However, there is a research gap on the line graph of interval-valued neutrosophic graphs. In this paper, we introduce the theory of an interval-valued neutrosophic line graph (IVNLG) and its application. In line with that, some mathematical properties such as weak vertex isomorphism, weak edge isomorphism, effective edge, and other properties of IVNLGs are proposed. In addition, we defined the vertex degree of IVNLG with some properties, and by presenting several theorems and propositions, the relationship between fuzzy graph extensions and IVNLGs was explored. Finally, an overview of the algorithm used to solve the problems and the practical application of the introduced graphs were provided.

Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design

Complex neutrosophic graphs are created by combining complex neutrosophic sets with graph theory ideas. This provides a flexible framework for tackling complex problem-solving circumstances. Various processes, such as union, join, and composition, are thoroughly investigated to improve the administration of complicated neutrosophic graphs. This research also looks into the area of complicated neutrosophic graph homeomorphisms, investigating the transformations and mappings that occur inside these structures. This investigation advances our knowledge of the intrinsic features and linkages found in complicated neutrosophic graphs. Finally, our methodology’s practical usefulness is demonstrated by its use in the design of hospital infrastructure. We illustrate the effectiveness of complicated neutrosophic graphs in addressing difficult design concerns and optimizing infrastructure solutions for practical deployment in this real-world scenario.

The connectivity indices concept of neutrosophic graph and their application of computer network, highway system and transport network flow

To address information ambiguities, this study suggests using neutrosophic sets as a tactical tool. Three membership functions (called Tr,In,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_r, I_n, $$\\end{document} and Fi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ F_i$$\\end{document}) that indicate an object’s degree of truth, indeterminacy, and false membership constitute the neutrosophic set. It becomes clear that the neutrosophic connectivity index (CIN) is an essential tool for solving practical problems, especially those involving traffic network flow. To capture uncertainties, neutrosophic graphs are used to represent knowledge at different membership levels. Two types of CINs,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$CIN_s,$$\\end{document} mean CIN and CIN, are investigated within the framework of neutrosophic graphs. In the context of neutrosophic diagrams, certain node types-such as neutrosophic neutral nodes, neutrosophic connectivity reducing nodes (NCRN) , and neutrosophic graph connectivity enhancing nodes (NCEN) , play important roles. We concentrate on two types of networks, specifically traffic network flow, to illustrate the real-world uses of CIN. By comparing results, one can see how junction removal affects network connectivity using metrics like Connectivity Indexes (CIN) and Average Connectivity Indexes (ACIN) . A few nodes in particular, designated by ACIN as Non-Critical Removal Nodes (NCRNs)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ (NCRN_s) $$\\end{document}, show promise for increases in average connectivity following removal. To fully comprehend traffic network dynamics and make the best decisions, it is crucial to take into account both ACIN and CIN insights. This is because different junctions have different effects on average and overall connectivity metrics.

Special irregular neutrosophic graphs

Recently, the neutrosophic graph has been introduced as an extension of fuzzy graphs and intuitionistic fuzzy graphs, which offers more compatibility and flexibility than these two types in modeling and structuring many actual issues. In this article, using neutrosophic highly strong arc, the new notions of (totally) special irregular, highly special irregular, strongly special irregular, neighborly special irregular and special arc-irregular of neutrosophic graphs are stated. Finally, one of their utilizations relevant to offering a fixed optimization model in decision making in diverse conditions is presented. In fact,we present a decision-making problem in real-world applied example which discusses the factors influencing a companys efficiency. The presented model is, in fact, a factor-based model wherein the impact score of each factor is divided into two types of direct and indirect influences, in which the concept of neutrosophic special dominating set plays a significant role.

The Energy of Interval-Valued Complex Neutrosophic Graph Structures: Framework, Application and Future Research Directions


 Graph structure is a developing field with many real-world applications and advancements, particularly effective frameworks for integrative problem-solving in computer networks and artificial intelligence systems. To define the idea of an Interval-Valued Complex Neutrosophic Graph Structure (IVCNGS), the concept of an Interval-Valued Complex Neutrosophic Set (IVCNS) is applied to the graph structure. Using the adjacency matrix to calculate the degree of vertex, we have defined some findings about the IVCNGS. Further, we compute the energy and Laplacian energy of IVCNGS. Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of IVCNGS, and we have discussed their application in IVCNGS. Finally, we develop an algorithm that clarifies the fundamental processes of the application.

Identifying Internet Streaming Services using Max Product of Complement in Neutrosophic Graphs

The complement of the highest result of multiplication of two neutrosophic graphs is determined in this study. In the complement of the maximum product of a neutrosophic graph, the degree of a vertex is investigated. The complement of the maximum product of two normal neutrosophic graphs has several results that are presented and proven. Finally, we have offered a neutrosophic graph application for locating an online streaming service using normalized Hamming distance.

On Neutrosophic Topological Spaces Generated by Single Value Neutrosophic Graph

The concept of a single-valued neutrosophic graph SVNS-G is recently studied, the bond between neutrosophic graph N-G and neutrosophic topological graph NT-G was my goal in this research, I try to find a relation on the vertices of the SVN-G to structure NT-G add some theorems and corollaries.

Fermatean Shortest Route Problem with Interval Fermatean Neutrosophic Fuzzy Arc Length: Formulation and a Modified Dijkstra’s Algorithm

Dijkstra’s algorithm (DA) is a very popular approach for finding the shortest route (SR) in the shortest route problem (SRP). The SRP becomes a challenging and complex problem in real life scenarios. The Fermatean neutrosophic set is a mathematical model that combines Fermatean sets with neutrosophic sets. It can handle the unclear, ambiguous, inconsistent, confusing, and uncertain information that comes from real-world problems. Decision-makers face difficulty accurately determining the precise membership (MG) and non membership levels due to the lack of appropriate data available. The FNS can handle this problem. In this study, we consider the interval FNS to describe the arc weight of a neutrosophic graph (NG). This SRP is called an interval Fermatean neutrosophic shortest route problem (IFNSRP). A modified DA is presented to solve this IFNSRP in an uncertain environment. The effectiveness of the presented method is illustrated with a numerical instance of a neutrosophic network.

Interval-valued Fermatean Neutrosophic Graph with Grey Wolf Optimization for Sarcasm Recognition on Microblogging Data

Game theory is more popular in competitive situations due to its importance in decision making. Several kinds of fuzzy sets can manage uncertainty in matrix games. Neutrosophic set theory has been instrumental in investigating ambiguity, complexity, inconsistency, and incompleteness in real-time issues. Nowadays, sarcastic comments on social media have become a general tendency. Sarcasm is frequently used by individuals to pester or taunt others. It is often conveyed via inflection, tonal stress in speech, or lexical, hyperbolic, and pragmatic features existing in the text. Sentiment Analysis (SA) is regarded as the data mining targets of sentiment organization of the client's criticisms obtainable in textual form. Sarcasm is a form of speech that states an individual's downside feeling through a positive term. Labeling sarcasm in characters is a dynamic task for Natural Language Processing to evade the misconception of sarcastic speeches as a verbatim declaration. The outcome of these kinds of sarcastic speeches is hard for the people and machines. Sarcasm has a considerable influence on the efficacy of SA techniques that are impacted by mendacious sentiments that frequently belong to sarcastic classes. This study introduces an Interval-valued Fermatean Neutrosophic Graph with Grey Wolf Optimization for Sentiment Analysis (IFeNG-GWOSA) on Microblogging Data. The IFeNG-GWOSA technique includes a sarcasm detection technique that categorizes words in sarcastic or non-sarcastic form. The initial phase is preprocessing, where the tokenization and stop word removal are implemented. Then, the preprocessed data is subjected to feature extraction, where the BERT word embedding is applied. The IFeNG model is used for sarcasm detection, and the grey wolf optimizer (GWO) generates its parameter selection technique. Lastly, the efficiency of the presented technique is compared with existing approaches under different measures

Study Some Methods To Measure The Reliability System Neutrosophically

Industry has developed greatly nowadays, and it has been accompanied by great complexity in machines and devices. Researches that seeks to obtain high efficiencies for these machines have emerged , such as reliability theory. Due to the verity and complexity of the machines, we resort to using the neutrosophic reliability that includes cases excluded from classical reliability. The aim of this paper is to define the neutrosophic parallel system and study neutrosophic methods of calculating the neutrosophic reliability, where the basic concept neutrosophic adjacency matrix of system are present by defined neutrosophic adjacency matrix of neutrosophic graph. Two methods for calculate the neutrosophic reliability are defined conformity to neutrosophic logic which are neutrosophic minimal path method and neutrosophic tracing method. some applications have been introduced.