We have compiled the list of Best Reference Books on Graph Theory subject. These books are used by students of top universities, institutes and colleges. Here is the full list of best books on Graph Theory along with reviews.
Kindly note that we have put a lot of effort into researching the best books on Graph Theory subject and came out with a recommended list of best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on “Graph Theory” as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
List of Graph Theory Books with author’s names, publishers, and an unbiased review as well as links to the Amazon website to directly purchase these books.
1. Advanced Graph Theory
1. “Introduction to Graph Theory” by Douglas B West
Book Review: This book provides a thorough introduction to graph theory that covers both the aspects i.e understanding the graphs and writing proofs about graphs. Algorithmic work verification is given more emphasis than the complexity of algorithms. The book provides an effective usage of examples, a number of interesting exercises with challenging examples, demonstration of concepts of trees and distances, matchings and factors, connectivity of graphs and paths, coloring of graphs, edges and cycles and planar graphs. This book is very useful for students studying computer science and mathematics.


2. “Graph Theory with Applications to Engineering and Computer Science” by Narsingh Deo
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Book Review: This book presents an insight of how graph theory concept is applied in the field of engineering, physical sciences, social sciences, linguistics and many other areas. The books describes how a graph can be used to represent a physical situation involving discrete objects and relationship among them. The topics included are basics, paths and circuits, trees, cut sets and vertices, vector spaces and matrix representation of graphs, graph coloring and covering. The book also includes problems on directed graphs, enumeration of graphs and computer programs.


3. “Graph Theory” by Frank Harary
Book Review: This book covers various concepts related to the subject of graph theory. The book therefore includes the historical background of graph theory where each concept and the result is clarified with the help of diagrams and figures. The book also contains appendices which provide the readers the diagrams of graphs, directed graphs and trees. The book also provides more importance to theorems rather than algorithms and its applications. The book also provides a comprehensive set of graphs in all the areas of graph theory. The book also provides a nice overview in the area of discrete mathematics.


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 excellent reference book for designers, manufacturing engineers, practitioners, managers, applied research workers, and students in mechanical, design, and industrial engineering fields.


5. “Groups Acting on Graphs” by Bela Bollobas
“Groups Acting on Graphs” Book Review: This book analyzes groups acting on low dimensional topological spaces with an algebraic approach. Equivariant loop, sphere theorems, accessibility of finitely presented groups, and characterization of Poincare duality groups are some of the important topics discussed in this book. Prerequisite knowledge of group theory, homological algebra, and algebraic topology is required to obtain the book’s full potential.


6. “Graph Theory : Proceedings of a Conference Held in Lagow, Poland, February 1013, 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 book showcases the variety of graph theoretical methods and its relation to combinatorics. It presents new information and special methods in an engaging method with lots of illustrations and examples. Honoring the pioneer of graph theory, Gerhard Ringel, this book serves as an open source guide to the extensive literature and encourages further research on graph theory and combinatorics.
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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 provides applications of graph theory. This book provides an introduction to the fundamentals of graph theory. Basic topics such as network flows, connectivity, trees, matching and factors, graph coloring, Hamiltonian graphs, and graph embeddings are explained with detailed proofs and solved examples. Replete with problems to practice on, this book is suitable for a quick overview of the subject and to help prepare for tests and exams. It gives thorough understanding of all the topics. The book contains a variety of examples. It also provides exercise questions along with the solutions for better understanding of the concepts.


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 offers a detailed coverage of pure and applied graph theory. In addition to examples, solved, and unsolved problems, the book also provides important definitions and bibliography for each chapter. This book is ideal for novices in the field as well as students studying mathematics, operations research, computer science and engineering courses.


2. Applied Graph Theory
1. “Introduction to Graph Theory” by Douglas B West
“Introduction to Graph Theory” Book Review: This book provides a thorough introduction to graph theory that covers both the aspects i.e understanding the graphs and writing proofs about graphs. Algorithmic work verification is given more emphasis than the complexity of algorithms. The book provides an effective usage of examples, a number of interesting exercises with challenging examples, demonstration of concepts of trees and distances, matchings and factors, connectivity of graphs and paths, coloring of graphs, edges and cycles and planar graphs. This book is very useful for students studying computer science and mathematics.


2. “Graph Theory” by Frank Harary
“Graph Theory” Book Review: This book covers various concepts related to the subject of graph theory. The book therefore includes the historical background of graph theory where each concept and the result is clarified with the help of diagrams and figures. It also contains appendices which provide the readers the diagrams of graphs, directed graphs and trees. It also provides more importance to theorems rather than algorithms and its applications. The book covers a comprehensive set of graphs in all the areas of graph theory while providing a nice overview in the area of discrete mathematics. This book is suitable for students and professionals who wish to know more about these fields.


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 deals with theorems and applications based on graph theory with special emphasis on constructions (consisting of formal proofs) and examples with applications. Replete with illustrations and exercises at the end of each chapter, this book is suitable for both undergraduate and postgraduate students in computer science/ computer applications, operational research, mathematics, and applied sciences.


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 IMA book is based on the proceedings of a workshop which was a part of the 198788 IMA program on APPLIED COMBINATORICS. Several fundamental concepts have been discussed in great detail such as interval graphs; qualitative stability; balanced signed graphs; RNA chains as “words” in a 4 letter alphabet; competition graphs or niche overlap graphs; social welfare functions; and semiorders – which arise in the applications of combinatorics and graph theory in the biological and social sciences. The book is arranged in such a way that for each concept, some basic results are presented, some recent results are given, and some open problems are discussed.


5. “The Fascinating World of Graph Theory” by Dr Ping Zhang Gary
“The Fascinating World of Graph Theory” Book Review: This book explores the world of graphs, i.e. mathematical structures showing relations between objects. Introducing fundamental concepts, the author introduces fundamental concepts of graph theory and presents classic problems such as the lights out puzzle. Each chapter contains math exercises and problems for readers to solve. Graph theory has a vast range of applications in biology, computer science, transportation science, etc. Hence, this book is a perfect read for professionals and students who wish to delve deeper into graph theory.


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 comprehensively covers the application of topology, graph theory, and related mathematical disciplines to metal clusters and coordination compounds. The main topics covered are – topology, graph theory and group theory, and their relationship to the properties of atomic orbitals and coordination polyhedra, its application to the structure and chemical bonding in diverse types of inorganic compounds, including boron cages, metal clusters, solid state materials, metal oxide derivatives, superconductors, icosahedral phases, and carbon cages (fullerenes). The book concludes with an introduction to the application of topology and graph theory for studying the dynamics of rearrangements in coordination and cluster polyhedra.


7. “Graph Theory for Programmers” by Evstigneev Kasyanov Vladimir
“Graph Theory for Programmers” Book Review: This book explores the basic algorithms and fundamental concepts involved in the vast field of algorithmic graph theory. It provides an indepth analysis of the most important type of graph in programming and informatics, i.e. highlevel and languageindependent descriptions of methods and algorithms in trees. This text is recommended for students in computer science, electronics, telecommunications, and control engineering. Researchers, mathematicians or specialists in software engineering, programming, discrete optimization, and operations research can also refer to this book.


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 explains the applications of graph theory in engineering and physical sciences. It describes trees and fundamental circuits. The book presents the matrix representation of graphs. It contains information about vector spaces of graphs, enumeration of graphs, graph theoretical algorithms and graphs in switching and coding theory. The book also gives inference on binetcauchy theorem and Sylvester’s law. The chapters included in this book are – Paths and Circuits; Trees and Fundamental Circuits; CutSets and CutVertices; Planar and Dual Graphs; Vector Spaces of a Graph; Matrix Representation of Graphs; Coloring; Covering and Partitioning; Directed Graphs; Enumeration of Graphs; Graph Theoretic Algorithms and Computer Programs; Graphs in Switching and Coding Theory; Electrical Network Analysis by Graph Theory; Graph Theory in Operations Research; and Survey of other Applications. This book is recommended for students and professionals from computer science and engineering backgrounds.


2. “Introduction to Graph Theory” by West
“Introduction to Graph Theory” Book Review: This book ranges from basic to advanced level of graph theory. It describes the basic algorithms of graph theory. The book helps in learning the structure of graphs. This book provides a number of examples for better understanding of the topic. The undergraduate and postgraduate students of mathematics and computer science will find this book useful.


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 book explains the basic concepts, theorems, examples and definitions from graph theory. It discusses the design and analysis of computer algorithms. The book gives the application of graph theory to the sciences.


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: The book explains the combinatorics and graph theory. This book helps in understanding planar graphs and matrix representation of graphs. It provides the concept of enumeration. The book gives the application of graphs in computer science. It contains various examples for easily understanding the topic.


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