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Fuzzy graph theory
Mathew S., Mordeson J., Malik D., Springer International Publishing, Cham, Switzerland, 2018. 320 pp. Type: Book (978-3-319714-06-6)
Date Reviewed: Aug 24 2018

Fuzzy graph theory is a recently developed field, and thus many research opportunities exist. This book is a very good and suitable option for readers who wish to either begin or continue their studies in different areas of fuzzy graph theory.

The book is divided into eight chapters. The first chapter is an overview of fuzzy set theory, fuzzy relations, and the related concepts used in subsequent chapters. Basic fuzzy graph terminology is introduced in the next chapter. It discusses the fuzzy analogue of graph-theoretic notions such as paths and cycles, connectedness, subgraphs, separability, graph operations, graph isomorphism, and so on. It establishes many interesting results and characterizations related to fuzzy graphs. Partial and strong partial subgraphs are also introduced and studied.

Chapter 3 discusses the connectivity of fuzzy graphs and related results. It begins with definitions of different types of edges and paths in fuzzy graphs; based on these definitions, some characterizations of fuzzy trees and fuzzy bridges are provided. These results include fuzzy vertex connectivity and fuzzy clusters of fuzzy graphs. Fuzzy analogues of Menger’s theorem are also provided here.

The fourth chapter is an extended study on blocks, critical blocks, and block graphs of fuzzy graphs. Connectivity transitive and cyclically transitive fuzzy graphs are also discussed. Some interesting results are provided with illustrations and applications.

Chapter 5 provides extended studies on connectivity in fuzzy graphs. It starts with definitions of connectedness and acyclic levels, and then covers concepts and results related to cycle connectivity, bonds and cutbonds, metrics, and detour distance.

The sixth chapter begins with a discussion of certain special sequences in fuzzy graphs, such as strong sequences, binary sequences, and zero sequences, and then covers saturation, intervals, and gates and gated sets.

Chapter 7, “Interval-Valued Fuzzy Graphs,” discusses operations and isomorphism on interval-valued fuzzy graphs, interval-valued fuzzy line graphs, balanced interval-valued fuzzy graphs, self-centered interval-valued fuzzy graphs, and irregularity in interval-valued fuzzy graphs.

The last chapter, “Bipolar Fuzzy Graphs,” covers the operations, isomorphism, and connectivity of bipolar fuzzy graphs, as well as strong bipolar fuzzy graphs, regular bipolar fuzzy graphs, and bipolar fuzzy line graphs.

The book is rich with relevant illustrations and real-life/practical problems, where the various topics are or can be applied. The book is a comprehensive and in-depth study, and the style of presentation is remarkable. These aspects make reading this book an absolute delight.

Reviewer:  Sudev Naduvath Review #: CR146217 (1811-0555)
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