Best books on graph theory and algorithms for knowledge enrichment and advancement

Graph theory is a theory of graph and is a mathematical representation of a network which describes the relationship between lines and points. It's a branch of mathematics and is one of the most important topics in discrete math and programming

You can apply graph theory in

• Structural field
• Functional field
• Effective connectivity matrices

1. Introduction to Graph Theory

Author: Richard J Trudeau
Published at: 11/01/2017
ISBN: 1684112311

Graph theory and mathematical logic

Mathematics is fun. Richard J Trudeau relates mathematics to graph and teaches you what mathematics is, how mathematics works. He will show you that math is a game with few rules and a massive amount of freedom of experimentation.

What's inside

• Introduction to Euclidean geometry as pure mathematics
• Graphs
• Planar graphs
• Euler's formula
• Platonic graphs
• Coloring
• The genus of a graph
• Euler walks and Hamilton walks.

So why the introduction to graph theory is very much useful: People will find their interest in graph theory as many practical problems can be represented by graphs. This book provides you with a basic understanding of graph theory with mathematics so it can be a magnificent book for mathematics lover. You will find almost everything like all the logic, proof and elements of a graph with exercises.

2. A First Course in Graph Theory (Dover Books on Mathematics)

Author: Gary Chartrand,Ping Zhang
Published at: 15/02/2012
ISBN: 0486483681
Well organized, clear notation with entertaining examples

It's a great self-study covering the fundamentals of graph theory with illustrations and the theorems are explained by their proofs.

A sound introductory textbook with

• Graph theory's history and biography
• Unique examples and lucid proofs
• Optional sections present interesting sidelights of graph theory
• Solutions for exercises, in addition to references, indexes, and a list of symbols
• A great understanding of data mining and graph databases.

Three appendixes

• Sets and logic
• Equivalence relations and functions
• Methods of proof.

3. Graph Theory (Graduate Texts in Mathematics)

Author: Reinhard Diestel
Published at: 31/10/2010
ISBN: 3642142788

Learn the core of the pure graph theory

This is a very deep book and can be called the heart of graph theory. It covers almost everything about graphs, including coloring, matching, flows etc. Theories are explained with complete proofs. If people are interested in systems science which often uses graph theory this book is for them.

This is a very reliable book containing

• Matching, covering and packing
• Connectivity
• Planar graphs
• Extremal graph theory
• Infinite graphs
• Ramsey theory for graphs
• Hamilton cycles
• Random graphs
• Graph minors.

Graph Theory is for knowledge enrichment and advancement

This book cannot be substituted with any other book on the present textbook market because it provides readers a very valuable and rich learning experience. beautifully written and proofs are given in detail.

4. Modern Graph Theory (Graduate Texts in Mathematics)

Author: Bela Bollobas
Published at: 12/08/2002
ISBN: 0387984887

Modern Graph Theory should be on the shelf of everyone working in graph theory

This book presents almost everything and connects the branches of pure mathematics to graph theory. There are many topics for anyone who does research in graph theory, combinatorics, and/or complexity theory like electrical networks, flows, connectivity and matching, extremal problems, coloring, Ramsey theory, random graphs, graphs, groups, and matrices, random walks on graphs, the Tutte polynomial with 600+ exercises.

This book also contains many important theorems

• Max-flow/min-cut theorem
• Szemerédis regularity lemma and its use
• Shelah's extension of the Hales-Jewett theorem
• Tutte polynomial and its cousins in knot theory

So we can conclude that graph theory should be part of the education of every serious student of mathematics and computer science.

5. Graph Theory (Graduate Texts in Mathematics)

Published at: 28/08/2008
ISBN: 1846289696

This book contains everything from basic concepts to advanced level. So this book is for those who are unfamiliar with graph theory and the students in mathematics and computer science as it provides a systematic treatment of the theory of graphs.

This book includes

• Structures
• Operations and relations
• Graph parameters
• A family of the graph.

If you want in the future to go deeply into your research this book provides you the necessary information.

6. Graph Theory: A Problem Oriented Approach (Maa Textbooks)

Author: Daniel A. Marcus
Published at: 01/06/2011
ISBN: 0883857723

An amazing book for anyone

This book is suitable as a college level text for mathematics, computer science, or engineering students as well as for a general education course at a liberal arts college, or for self-study.

Graph Theory presents you a

• Series of approximately 360 strategically placed problems with connecting text
• 280 additional problems that are intended to be used as homework assignments

Coverage contains

• Problems of graph theory
• Basic concepts
• Isomorphic graphs
• Bipartite graphs
• Trees and forests
• Spanning tree algorithms
• Euler paths
• Hamilton paths and cycles
• Planar graphs
• Independence and covering
• Connections and obstructions
• Vertex coloring
• Edge coloring
• Matching theory for bipartite graphs
• Applications of matching theory
• Cycle-free digraphs
• Network flow theory
• Flow problems with lower bounds

7. Graph Theory with Applications to Engineering and Computer Science (Dover Books on Mathematics)

Author: Narsingh Deo
Published at: 17/08/2016
ISBN: 0486807932

Big areas in graph theory

This book solves many interesting problems. Whether you are a professional in graph theory or not this book helps you a lot by covering paths and circuits, trees and fundamental circuits, planar and dual graphs, vector spaces of a graph, matrix representation of graphs, coloring, covering, and partitioning, directed graphs, graph theory algorithms and computer programs, graphs in switching  and coding theory, electrical network analysis by graph theory, graph theory in operations research, survey of other applications etc.

There are also two appendix

1. Binet-Cauchy theorem
2. Nullity of a matrix and Sylvester's LawIndex

8. Extremal Graph Theory (Dover Books on Mathematics)

Author: Bela Bollobas,Mathematics
Published at: 04/06/2004
ISBN: 0486435962

Very good companion

This book is very dense and is valuable for both research students and undergraduate students of mathematics. It provides text features, complete proofs for almost all of its results. There are also some interesting open problems.

Extremal graph theory encompasses a diverse array of problem-solving methods

• Applications to economics
• Computer science and
• Optimization theory.

9. Graph Theory (Dover Books on Mathematics)

Author: Ronald Gould
Published at: 21/11/2012
ISBN: 0486498069
Many materials about graph theory with a lot of algorithms

An excellent self-study book with many exercises, excellent figures, and includes both algorithmic and theoretical problems. By reading this book you will be able to translate some algorithms of the book in the Scheme programming language. The algorithm makes the graph theory very clear and easy to understand.

Ronald Gould covers following topics to make the graph theory more clear

• Graphs
• Paths and searching
• Trees and networks
• Cycles and circuits
• Planarity
• Matchings
• Independence
• Special topics and applications
• Extremal theory

10. The Theory of Graphs (Dover Books on Mathematics)

Author: Claude Berge,Mathematics
Published at: 04/09/2001
ISBN: 0486419754

Concise and well-written text

A great book which describes graph theory and the way to apply its principles in methods both formal and abstract. The author covers the theory's broad range of applications, a versatile mathematical technique appropriate to the behavioral sciences, information theory, cybernetics with practical examples.

Sorted from easy to hard

This book is working as an easy to understand reference for the reader as it is sorted from easy to hard. The author begins with the simplest theorems and gradually builds the more complex theorems.

Thanks for reading this post. If you have any opinion don't hesitate to comment here. Also please subscribe our newsletter to get more updates.