A Reconsideration Of Advanced Concepts In Neutrosophic Graphs Smart Zero Divisor Layered Weak Semi And Chemical Graphs
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A Reconsideration Of Advanced Concepts In Neutrosophic Graphs Smart Zero Divisor Layered Weak Semi And Chemical Graphs
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2024-11-01
A Reconsideration Of Advanced Concepts In Neutrosophic Graphs Smart Zero Divisor Layered Weak Semi And Chemical Graphs written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
One of the most powerful tools in graph theory is the classification of graphs into distinct classes based on shared properties or structural features. Over time, many graph classes have been introduced, each aimed at capturing specific behaviors or characteristics of a graph. Neutrosophic Set Theory, a method for handling uncertainty, extends fuzzy logic by incorporating degrees of truth, indeterminacy, and falsity. Building on this framework, Neutrosophic Graphs [9,84,135] have emerged as significant generalizations of fuzzy graphs. In this paper, we extend several classes of fuzzy graphs to Neutrosophic graphs and analyze their properties.
Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2024-11-01
Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels in handling uncertainty, while set theory has evolved with concepts such as fuzzy and neutrosophic sets, which enable the modeling of complex real-world uncertainties by addressing truth, indeterminacy, and falsehood. These advancements, when combined with graph theory, give rise to novel forms of uncertain sets in "graphized" structures, including hypergraphs and superhypergraphs. Innovations such as Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing both theoretical and practical boundaries. The synthesis of combinatorics, set theory, and graph theory in this volume provides a robust framework for addressing the complexities and uncertainties inherent in both mathematical and real-world systems, paving the way for future research and application. In the first chapter, “A Review of the Hierarchy of Plithogenic, Neutrosophic, and Fuzzy Graphs: Survey and Applications”, the authors investigate the interrelationships among various graph classes, including Plithogenic graphs, and explore other related structures. Graph theory, a fundamental branch of mathematics, focuses on networks of nodes and edges, studying their paths, structures, and properties. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, representing the level of uncertainty. The Turiyam Neutrosophic Graph is introduced as an extension of both Neutrosophic and Fuzzy Graphs, while Plithogenic graphs offer a potent method for managing uncertainty. The second chapter, “Review of Some Superhypergraph Classes: Directed, Bidirected, Soft, and Rough”, examines advanced graph structures such as directed superhypergraphs, bidirected hypergraphs, soft superhypergraphs, and rough superhypergraphs. Classical graph classes include undirected graphs, where edges lack orientation, and directed graphs, where edges have specific directions. Recent innovations, including bidirected graphs, have sparked ongoing research and significant advancements in the field. Soft Sets and their extension to Soft Graphs provide a flexible framework for managing uncertainty, while Rough Sets and Rough Graphs address uncertainty by using lower and upper approximations to handle imprecise data. Hypergraphs generalize traditional graphs by allowing edges, or hyperedges, to connect more than two vertices. Superhypergraphs further extend this by allowing both vertices and edges to represent subsets, facilitating the modeling of hierarchical and group-based relationships. The third chapter, “Survey of Intersection Graphs, Fuzzy Graphs, and Neutrosophic Graphs”, explores the intersection graph models within the realms of Fuzzy Graphs, Intuitionistic Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. The chapter highlights their mathematical properties and interrelationships, reflecting the growing number of graph classes being developed in these areas. Intersection graphs, such as Unit Square Graphs, Circle Graphs, and Ray Intersection Graphs, are crucial for understanding complex graph structures in uncertain environments. The fourth chapter, “Fundamental Computational Problems and Algorithms for SuperHyperGraphs”, addresses optimization problems within the SuperHypergraph framework, such as the SuperHypergraph Partition Problem, Reachability, and Minimum Spanning SuperHypertree. The chapter also adapts classical problems like the Traveling Salesman Problem and the Chinese Postman Problem to the SuperHypergraph context, exploring how hypergraphs, which allow hyperedges to connect more than two vertices, can be used to solve complex hierarchical and relational problems. The fifth chapter, “A Short Note on the Basic Graph Construction Algorithm for Plithogenic Graphs”, delves into algorithms designed for Plithogenic Graphs and Intuitionistic Plithogenic Graphs, analyzing their complexity and validity. Plithogenic Graphs model multi-valued attributes by incorporating membership and contradiction functions, offering a nuanced representation of complex relationships. The sixth chapter, “Short Note of Bunch Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs”, generalizes traditional graph theory by representing nodes as groups (bunches) rather than individual entities. This approach enables the modeling of both competition and collaboration within a network. The chapter explores various uncertain models of bunch graphs, including Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. In the seventh chapter, “A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs”, the authors extend several fuzzy graph classes to Neutrosophic graphs and analyze their properties. Neutrosophic Graphs, a generalization of fuzzy graphs, incorporate degrees of truth, indeterminacy, and falsity to model uncertainty more effectively. The eighth chapter, “Short Note of Even-Hole-Graph for Uncertain Graph”, focuses on Even-Hole-Free and Meyniel Graphs analyzed within the frameworks of Fuzzy, Neutrosophic, Turiyam Neutrosophic, and Plithogenic Graphs. The study investigates the structure of these graphs, with an emphasis on their implications for uncertainty modeling. The ninth chapter, “Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs”, explores planar and outerplanar graphs, as well as apex graphs, within the contexts of fuzzy, neutrosophic, Turiyam Neutrosophic, and plithogenic graphs. The chapter examines how these types of graphs are used to model uncertain parameters and relationships in mathematical and real-world systems. The tenth chapter, “General Plithogenic Soft Rough Graphs and Some Related Graph Classes”, introduces and explores new concepts such as Turiyam Neutrosophic Soft Graphs and General Plithogenic Soft Graphs. The chapter also examines models of uncertain graphs, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, all designed to handle uncertainty in diverse contexts. The eleventh chapter, “Survey of Trees, Forests, and Paths in Fuzzy and Neutrosophic Graphs”, provides a comprehensive study of Trees, Forests, and Paths within the framework of Fuzzy and Neutrosophic Graphs. This chapter focuses on classifying and analyzing graph structures like trees and paths in uncertain environments, contributing to the ongoing development of graph theory in the context of uncertainty.
Some Results On The Graph Theory For Complex Neutrosophic Sets
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Author : Shio Gai Quek
language : en
Publisher: Infinite Study
Release Date :
Some Results On The Graph Theory For Complex Neutrosophic Sets written by Shio Gai Quek and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graph called complex neutrosophic graphs of type 1 (abbr. CNG1). We then present a matrix representation for it and study some properties of this new concept.
Single Valued Neutrosophic Graphs
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Author : Muhammad Akram
language : en
Publisher: Springer
Release Date : 2018-12-30
Single Valued Neutrosophic Graphs written by Muhammad Akram and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-30 with Mathematics categories.
This book addresses single-valued neutrosophic graphs and their applications. In addition, it introduces readers to a number of central concepts, including certain types of single-valued neutrosophic graphs, energy of single-valued neutrosophic graphs, bipolar single-valued neutrosophic planar graphs, isomorphism of intuitionistic single-valued neutrosophic soft graphs, and single-valued neutrosophic soft rough graphs. Divided into eight chapters, the book seeks to remedy the lack of a mathematical approach to indeterminate and inconsistent information. Chap. 1 presents a concise review of single-valued neutrosophic sets, while Chap. 2 explains the notion of neutrosophic graph structures and explores selected properties of neutrosophic graph structures. Chap. 3 discusses specific bipolar neutrosophic graphs. Chap. 4 highlights the concept of interval-valued neutrosophic graphs, while Chap. 5 presents certain notions concerning interval-valued neutrosophic graph structures. Chap. 6 addresses the concepts of rough neutrosophic digraphs and neutrosophic rough digraphs. Chap. 7 focuses on the concepts of neutrosophic soft graphs and intuitionistic neutrosophic soft graphs, before Chap. 8 rounds out the book by considering neutrosophic soft rough graphs.
Operations On Single Valued Neutrosophic Graphs
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Author : Muhammad Akram
language : en
Publisher: Infinite Study
Release Date :
Operations On Single Valued Neutrosophic Graphs written by Muhammad Akram and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The concept of neutrosophic sets can be utilized as a mathematical tool to deal with imprecise and unspecified information. In this paper, we apply the concept of single-valued neutrosophic sets to graphs. We introduce the notion of single-valued neutrosophic graphs, and present some fundamental operations on single-valued neutrosophic graphs. We explore some interesting properties of single-valued neutrosophic graphs by level graphs. We highlight some flaws in the definitions of Broumi et al. [10] and Shah-Hussain [18]. We also present an application of single-valued neutrosophic graphs in social network.
On Neutrosophic Vague Graphs
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Author : S. Satham Hussain
language : en
Publisher: Infinite Study
Release Date :
On Neutrosophic Vague Graphs written by S. Satham Hussain and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this work, the new concept of neutrosophic vague graphs are introduced form the ideas of neutrosophic vague sets. Moreover, some remarkable properties of strong neutrosophic vague graphs, complete neutrosophic vague graphs and self-complementary neutrosophic vague graphs are investigated and the proposed concepts are described with suitable examples.
Isolated Single Valued Neutrosophic Graphs
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Author : Said Broumi
language : en
Publisher: Infinite Study
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Isolated Single Valued Neutrosophic Graphs written by Said Broumi and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Many results have been obtained on isolated graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph.
Operations Of Single Valued Neutrosophic Coloring
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Author : A. Rohini
language : en
Publisher: Infinite Study
Release Date :
Operations Of Single Valued Neutrosophic Coloring written by A. Rohini and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Smarandache introduced the concept of Neutrosophic which deals with membership, non-membership and indeterminacy values. Wang discussed the Single Valued Neutrosophic sets in 2010. Single Valued Neutrosophic graph was introduced by Broumi and in 2019 Single Valued Neutrosophic coloring was introduced. In this paper, some properties of the Single Valued Neutrosophic Coloring of Strong Single Valued Neutrosophic graph, Complete Single Valued Neutrosophic graph and Complement of Single Valued Neutrosophic graphs are discussed.
Self Centered Single Valued Neutrosophic Graphs
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Author : V. Krishnaraj
language : en
Publisher: Infinite Study
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Self Centered Single Valued Neutrosophic Graphs written by V. Krishnaraj and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper, we introduce the concepts of length, distance, eccentricity, radius, diameter, status, total status, median and central vertex of a single valued neutrosophic graph. We present the concept of self-centered single valued neutrosophic graph. We investigated some properties of self-centered single valued neutrosophic graphs.
Accessible Single Valued Neutrosophic Graphs
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Author : M. Hamidi
language : en
Publisher: Infinite Study
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Accessible Single Valued Neutrosophic Graphs written by M. Hamidi and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
This paper derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via strong equivalence relation. We show that any weak single-valued neutrosophic graph is a derived single-valued neutrosophic graph and any linear weak single-valued neutrosophic tree is an extendable linear single-valued neutrosophic tree.