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2018 | Buch

Graphs Under Neutrosophic Environment Kapitel lesen Erstes Kapitel lesen

Single-Valued Neutrosophic Graphs

verfasst von: Prof. Muhammad Akram

Verlag: Springer Singapore

Buchreihe : Infosys Science Foundation Series

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Graphs Under Neutrosophic Environment
Abstract
In this chapter, we first present a concise review of neutrosophic sets. Then we present certain types of single-valued neutrosophic graphs (neutrosophic graphs, for short), including regular neutrosophic graphs, totally regular neutrosophic graphs, edge regular neutrosophic graphs, irregular neutrosophic graphs, highly totally irregular neutrosophic graphs, strongly totally irregular neutrosophic graphs, neighbourly edge irregular neutrosophic graphs and strongly edge irregular neutrosophic graphs. We describe applications of neutrosophic graphs. We also present energy of neutrosophic graphs with applications. This chapter is due to [27, 124, 167, 176].
Muhammad Akram
Chapter 2. Graph Structures Under Neutrosophic Environment
Abstract
A single-valued neutrosophic graph structure (neutrosophic graph structure, for short) is a generalization of neutrosophic graph. In this chapter, we present the notion of neutrosophic graph structures and explore some properties of neutrosophic graph structures. Moreover, we discuss the concept of \(\phi \)-complement of neutrosophic graph structure and present certain operations of neutrosophic graph structures elaborated with examples. Further, we discuss some applications of neutrosophic graph structures in decision-making. This chapter is due to [33, 34, 151].
Muhammad Akram
Chapter 3. Certain Bipolar Neutrosophic Graphs
Abstract
In this chapter, we present a concise review of bipolar neutrosophic sets. We present operations on bipolar single-valued neutrosophic graphs (bipolar neutrosophic graphs, for short). We discuss certain bipolar neutrosophic graphs, including totally regular bipolar neutrosophic graphs, totally irregular bipolar single-valued neutrosophic graphs and edge regular bipolar neutrosophic graphs. We study domination in bipolar neutrosophic graphs. We present bipolar neutrosophic planar graphs and bipolar neutrosophic line graphs. We also describe some applications of bipolar neutrosophic graphs. This chapter is due to [19, 25].
Muhammad Akram
Chapter 4. Graphs Under Interval-Valued Neutrosophic Environment
Abstract
In this chapter, we present the concept of interval-valued neutrosophic competition graphs. We then discuss certain types, including k-competition interval-valued neutrosophic graphs, p-competition interval-valued neutrosophic graphs and m-step interval-valued neutrosophic competition graphs. Moreover, we present the concept of m-step interval-valued neutrosophic neighbourhood graphs. This chapter is due to [12].
Muhammad Akram
Chapter 5. Interval-Valued Neutrosophic Graph Structures
Abstract
In this chapter, we present certain notions of interval-valued neutrosophic graph structures. We elaborate the concepts of interval-valued neutrosophic graph structures with examples. Moreover, we discuss the concept of \(\varphi \)-complement of an interval-valued neutrosophic graph structure. Finally, we describe some related properties, including \(\varphi \)-complement, totally self-complementary and totally strong self-complementary, of interval-valued neutrosophic graph structures. This chapter is due to [35].
Muhammad Akram
Chapter 6. Graphs Under Neutrosophic Hybrid Models
Abstract
Rough sets and single-valued neutrosophic sets are mathematical models to deal with incomplete and vague information. These two models can be combined into two frameworks for modelling and processing incomplete information in information systems. Thus, single-valued neutrosophic rough set model and rough single-valued neutrosophic set model are hybrid models, which give more precision, flexibility and compatibility to the system as compared to the classic and fuzzy models. In this chapter, we present rough single-valued neutrosophic digraphs (rough neutrosophic digraphs, for short) and neutrosophic rough digraphs and describe methods of their construction. We consider the concept of self-complementary rough neutrosophic digraphs. We discuss regular neutrosophic rough digraphs. We also give a comparative analysis of rough neutrosophic digraphs and neutrosophic rough digraphs.
Muhammad Akram
Chapter 7. Graphs Under Neutrosophic Soft Environment
Abstract
In this chapter, we present concepts of neutrosophic soft graphs and intuitionistic neutrosophic soft graphs. We describe methods of their construction. We consider applications of neutrosophic soft graphs and intuitionistic neutrosophic soft graphs. This chapter is due to [22, 23].
Muhammad Akram
Chapter 8. Neutrosophic Soft Rough Graphs
Abstract
Neutrosophic soft rough set model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. We present the concept of neutrosophic soft rough graphs and describe different methods of their construction. We develop an efficient algorithm of our method to solve decision-making problems.
Muhammad Akram
Backmatter
Metadaten
Titel
Single-Valued Neutrosophic Graphs
verfasst von
Prof. Muhammad Akram
Copyright-Jahr
2018
Verlag
Springer Singapore
Electronic ISBN
978-981-13-3522-8
Print ISBN
978-981-13-3521-1
DOI
https://doi.org/10.1007/978-981-13-3522-8

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