Essential Graph Theory

This textbook is meant for mathematics, computer science, and engineering undergraduates pursuing studies in graph theory and algorithms.

This textbook is ideal for undergraduates of computer science, mathematics, and engineering studying graph theory and algorithms. It combines theory, step-by-step illustrations, and pseudocodes to transform complex concepts into accessible knowledge. It includes real-world and illustrative examples, clear explanations, and chapter-wise exercises.Designed for undergraduate students of computer science, mathematics, and engineering, this book provides the tools and understanding needed to master graph theory and algorithms. It offers a strong theoretical foundation, detailed pseudocodes, and a range of real-world and illustrative examples to bridge the gap between abstract concepts and practical applications. Clear explanations and chapter-wise exercises support ease of comprehension for learners. The text begins with the basic properties of graphs and progresses to topics such as trees, connectivity, and distances in graphs. It also covers Eulerian and Hamiltonian graphs, matchings, planar graphs, and graph colouring. The book concludes with discussions on independent sets, the Ramsey theorem, directed graphs and networks. Concepts are introduced in a structured manner, with appropriate context and support from mathematical language and diagrams. Algorithms are explained through rules, reasoning, pseudocode, and relevant examples.