A First Course in Graph Theory

This undergraduate textbook presents fundamental concepts in graph theory through a systematic and gradual progression. The authors cover essential topics including trees, connectivity, paths, matchings, colorings, and planarity. The book includes over 1,200 exercises ranging from straightforward applications to challenging problems that develop deeper understanding. Each chapter contains detailed examples, carefully chosen definitions, and clear explanations of key theorems. Mathematical proofs are presented with rigor while maintaining accessibility for students new to graph theory. The text emphasizes discrete mathematics and algorithmic thinking throughout its treatment of graph-theoretical concepts. This text serves as both an introduction to abstract mathematical thinking and a foundation for further study in discrete mathematics and theoretical computer science. The authors' approach highlights the elegant connections between graph theory and real-world applications.

Readers appreciate this text as an introductory graph theory resource that balances rigor with accessibility. Students note the clear progression from basic concepts to more complex topics, with one reviewer highlighting the "well-chosen examples that build understanding step by step." Liked: - Extensive exercise sets with varying difficulty levels - Clear proofs and explanations - Strong focus on definitions and fundamentals - High-quality illustrations and diagrams Disliked: - Some sections lack sufficient examples - More advanced topics receive limited coverage - Exercise solutions not included - Price point considered high by students Ratings: Goodreads: 4.19/5 (21 ratings) Amazon: 4.3/5 (15 reviews) A mathematics graduate student on Amazon noted: "The text excels at building foundational knowledge but could include more real-world applications." Multiple reviewers mentioned the book serves better as a teaching text than for self-study, citing the absence of solutions as a limitation for independent learners.

Introduction to Graph Theory by Richard J. Trudeau This text presents graph theory fundamentals through historical context and connections to topology, making it a natural complement to Chartrand's approach.

Graph Theory by Ronald Gould The book covers similar introductory material with additional emphasis on algorithms and applications in computer science.

Graph Theory with Applications by J.A. Bondy, U.S.R. Murty This text delves deeper into theoretical aspects while maintaining accessibility for first-course students.

Graph Theory and Its Applications by Jonathan L. Gross, Jay Yellen The text provides extensive coverage of applications in engineering and computer science while building on the same foundational concepts.

Graphs & Digraphs by Gary Chartrand, Linda Lesniak, Ping Zhang This book serves as a natural progression from A First Course in Graph Theory, exploring more advanced concepts with the same pedagogical approach.

🔵 Graph Theory, the subject of this textbook, was born from Leonhard Euler's solution to the famous Seven Bridges of Königsberg problem in 1736, marking the first time a geometric problem was solved by converting it into a graph. 🔵 Author Gary Chartrand has authored or co-authored over 275 research papers and several books in graph theory, making him one of the most prolific writers in the field. 🔵 This textbook grew out of lecture notes from courses taught at Western Michigan University, where both authors served as professors in the Mathematics Department. 🔵 The book's approach is unique in that it requires no previous knowledge of graph theory or advanced mathematics, making it accessible to students as early as high school level. 🔵 Graph theory, as presented in this book, has practical applications in diverse fields including computer networks, social media algorithms, molecular biology, and even dating apps that use matching algorithms based on graph theory concepts.