**Best Reference Books on Graph Theory**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Graph Theory Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Graph Theory below.

## 1. Advanced Graph Theory

1."Introduction to Graph Theory" by Douglas B West
Book Review: This book offers a comprehensive introduction to graph theory, covering both understanding graphs and writing proofs about them. While the complexity of algorithms is briefly discussed, the primary focus is on algorithmic work verification. The book is rich in examples that effectively illustrate key concepts, and features numerous challenging exercises that will challenge students. It explores a variety of topics, including trees and distances, matchings and factors, connectivity of graphs and paths, coloring of graphs, edges and cycles, and planar graphs. This book is highly recommended for students of computer science and mathematics.
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2."Graph Theory with Applications to Engineering and Computer Science" by Narsingh Deo
Book Review: This book explores the diverse applications of graph theory across a wide range of fields, including engineering, physical sciences, social sciences, linguistics, and beyond. It demonstrates how graphs can effectively represent discrete objects and their relationships within physical situations. The book covers a range of topics, including fundamental concepts, paths and circuits, trees, cut sets and vertices, vector spaces, matrix representation of graphs, graph coloring, and covering. Additionally, the book presents a variety of problems involving directed graphs, graph enumeration, and computer programming.
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3."Graph Theory" by Frank Harary
Book Review: This book provides historical background on graph theory, accompanied by diagrams and figures that clarify each concept and result. Appendices are included, containing diagrams of graphs, directed graphs, and trees. The book emphasizes theorems over algorithms and their applications and offers a comprehensive collection of graphs covering all areas of graph theory. Additionally, the book provides a helpful overview of discrete mathematics.
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4."Decision Making in Manufacturing Environment Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods" by Rao R Venkata Rao
“Decision Making in Manufacturing Environment using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods: Volume 2” Book Review: This book explains the theory and details of applications of MADM methods in a comprehensive manner. A range of methods are covered including Grey Relational Analysis (GRA), Analytic Hierarchy Process (AHP), VIšekriterijumsko KOmpromisno Rangiranje (VIKOR), COmplex PRoportional Assessment (COPRAS), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), ELimination Et Choix Traduisant la Realité (ELECTRE), Data Envelopment Analysis (DEA), Preference Ranking METHod for Enrichment Evaluations (PROMETHEE), UTility Additive (UTA), and Ordered Weighted Averaging (OWA). This serves as an ideal reference book for designers, manufacturing engineers, practitioners, managers, applied research workers, and students in mechanical, design, and industrial engineering fields.
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5."Groups Acting on Graphs" by Bela Bollobas
“Groups Acting on Graphs” Book Review: This book employs an algebraic approach to analyzing groups that act on low-dimensional topological spaces. Topics covered include equivariant loop and sphere theorems, the accessibility of finitely presented groups, and the characterization of Poincare duality groups. Readers should have a prerequisite understanding of group theory, homological algebra, and algebraic topology to fully engage with this book.
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6."Graph Theory : Proceedings of a Conference Held in Lagow, Poland, February 10-13, 1981" by M Borowiecki | |

7."Topics in Combinatorics and Graph Theory: Essays in Honour of Gerhard Ringel" by Rudolf Henn and Rainer Bodendiek
“Topics in Combinatorics and Graph Theory: Essays in Honour of Gerhard Ringel” Book Review: This engaging book explores the diverse range of graph theoretical methods and their relationship to combinatorics. Featuring numerous illustrations and examples, the book presents new information and special methods. As a tribute to the pioneering work of Gerhard Ringel, the book serves as an open-source guide to the extensive literature on graph theory and combinatorics, encouraging further research in these fields.
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8."Schaum's Outline of Graph Theory" by V K Balakrishnan
“Schaum’s Outlines of Graph Theory” Book Review: This book offers practical applications of graph theory, while also introducing the fundamental concepts of the subject. Topics such as network flows, connectivity, trees, matching and factors, graph coloring, Hamiltonian graphs, and graph embeddings are explained in detail, complete with proofs and solved examples. With numerous practice problems included, the book is an ideal resource for a quick overview of the subject, test and exam preparation, and a thorough understanding of the topics. The book features a variety of examples and exercise questions with solutions for improved comprehension.
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9."Handbook of Graph Theory (Discrete Mathematics and Its Applications)" by Jonathan L Gross and Jay Yellen
“Handbook of Graph Theory (Discrete Mathematics and its Applications)” Book Review: This book provides a comprehensive coverage of pure and applied graph theory. Each chapter includes important definitions, examples, solved and unsolved problems, and a bibliography. This resourceful book serves as an excellent guide to anyone interested in learning about graph theory.
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## 2. Applied Graph Theory

1."Introduction to Graph Theory" by Douglas B West
“Introduction to Graph Theory” Book Review: The book offers a comprehensive initiation to graph theory, encompassing the two major components of comprehending graphs and composing proofs regarding graphs. Emphasis is placed more on the algorithmic validation of work than on the intricacies of algorithms themselves. The book effectively employs a diverse range of examples and presents numerous intriguing exercises that feature challenging instances. It also includes demonstrations of various concepts, such as trees and distances, matchings and factors, connectivity of graphs and paths, the coloring of graphs, edges and cycles, and planar graphs.
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2."Graph Theory" by Frank Harary
“Graph Theory” Book Review: This book delves into the historical development of graph theory and uses diagrams and figures to explain its concepts and results. It includes appendices that contain diagrams of graphs, directed graphs, and trees. The book emphasizes theorems over algorithms and their applications, and covers a broad range of graphs in all areas of graph theory, while also providing an overview of discrete mathematics. It is a useful resource for students and professionals seeking to deepen their understanding of these fields.
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3."Graph Theory with Algorithms and Its Applications: In Applied Science and Technology" by Santanu Saha Ray
“Graph Theory with Algorithms and its Applications: In Applied Science and Technology” Book Review: This book provides a detailed coverage of graph theory, emphasizing on theorems and their practical applications through formal proofs and examples. It includes a variety of illustrations and exercises at the end of each chapter, making it a suitable reference for undergraduate and postgraduate students in computer science, computer applications, operational research, mathematics, and applied sciences.
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4."Applications of Combinatorics and Graph Theory to the Biological and Social Sciences" by Fred Roberts
“Applications of Combinatorics and Graph Theory to the Biological and Social Sciences” Book Review: This book is based on the proceedings of a workshop that was part of the 1987-88 IMA program on APPLIED COMBINATORICS, and it extensively covers several fundamental concepts. These concepts include interval graphs, qualitative stability, balanced signed graphs, RNA chains represented as “words” in a 4-letter alphabet, competition graphs or niche overlap graphs, social welfare functions, and semi-orders. All these concepts are important in the applications of combinatorics and graph theory in the biological and social sciences. The book presents basic results, recent advances, and open problems for each concept in a clear and organized manner. It is a valuable resource for researchers, students, and professionals in these fields.
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5."The Fascinating World of Graph Theory" by Dr Ping Zhang Gary
“The Fascinating World of Graph Theory” Book Review: This book is a comprehensive guide to graph theory, which is a mathematical framework used to represent relationships between objects. The author covers fundamental concepts in graph theory and presents classic problems, including the lights out puzzle. Each chapter includes mathematical exercises and problems for readers to solve. The applications of graph theory are extensive and include fields such as biology, computer science, and transportation science. As a result, this book is an ideal resource for professionals and students who want to gain a deeper understanding of graph theory.
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6."Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry" by King King
“Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry” Book Review: This book provides a comprehensive examination of how topology, graph theory, and related mathematical disciplines are applied to metal clusters and coordination compounds. The book covers various topics, including topology, graph theory, and group theory, and their connection to the properties of atomic orbitals and coordination polyhedra. The book also explores their application to understanding the structure and chemical bonding in different types of inorganic compounds, such as boron cages, metal clusters, solid state materials, metal oxide derivatives, superconductors, icosahedral phases, and carbon cages (fullerenes). The book concludes by introducing the application of topology and graph theory for investigating the dynamics of rearrangements in coordination and cluster polyhedra.
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7."Graph Theory for Programmers" by Evstigneev Kasyanov Vladimir
“Graph Theory for Programmers” Book Review: This book is a comprehensive guide to algorithmic graph theory, covering basic algorithms and fundamental concepts in the field. It provides an in-depth analysis of the most important type of graph used in programming and informatics: trees. The book offers high-level, language-independent descriptions of methods and algorithms in trees. It is recommended for students studying computer science, electronics, telecommunications, and control engineering. Additionally, researchers, mathematicians, and specialists in software engineering, programming, discrete optimization, and operations research can benefit from this book.
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## 3. Advance Graph Theory and Combinatorics

1."Graph Theory with Applications to Engineering and Computer Science" by Deo and Narsingh
“Graph Theory with Applications to Engineering and Computer Science” Book Review: This book explores the applications of graph theory in engineering and physical sciences, covering topics such as trees, circuits, matrix representation of graphs, vector spaces, enumeration, algorithms, and graphs in switching and coding theory. It also discusses binet-cauchy theorem and Sylvester’s law. The book is recommended for students and professionals in computer science and engineering. Chapters include Paths and Circuits, Cut-Sets and Cut-Vertices, Planar and Dual Graphs, Coloring, Covering and Partitioning, Directed Graphs, Graph Theoretic Algorithms, Graph Theory in Operations Research, and more.
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2."Introduction to Graph Theory" by West
“Introduction to Graph Theory” Book Review: This book on graph theory covers a wide range of topics, from beginner to advanced levels. It explains the fundamental algorithms used in graph theory and helps readers understand the structure of graphs. The book includes numerous examples to aid in comprehension, making it a valuable resource for undergraduate and postgraduate students studying mathematics and computer science.
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3."Invitation to Graph Theory" by Arumugam | |

4."Graph Theory: Modeling, Applications and Algorithms" by Agnarsson
“Graph Theory: Modeling, Applications and Algorithms” Book Review: This is an informative and practical book that offers a broad overview of graph theory. The book includes nine chapters that cover topics such as basic graph properties, connectivity, planarity, graph coloring, algorithms, and network flows. Each chapter features numerous examples, exercises, and practical applications, making the book ideal for both students and practitioners. This book is a must-read for anyone seeking to gain a comprehensive understanding of graph theory and its applications.
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5."Introduction to Graph Theory" by Gary Chartrand and Ping Zhang | |

6."Combinatorics and Graph Theory" by S B Singh
“Combinatorics and Graph Theory” Book Review: This book covers the topics of combinatorics and graph theory, including an explanation of planar graphs and matrix representations of graphs. It also includes the concept of enumeration and explores the applications of graphs in computer science. The book is filled with numerous examples to facilitate comprehension of the subject matter. This book is a valuable resource for those seeking to gain a deeper understanding of combinatorics and graph theory.
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