Introduction to Graph Theory, 2nd Edition
by Douglas B. West · Prentice Hall / Pearson
Proof-centred undergraduate text with 1296 exercises spanning trees and distance, matchings and factors, connectivity and paths, colouring, edges and cycles, planarity, and directed graphs. Emphasises constructing and verifying graph proofs over algorithmic complexity.
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Graphs and Digraphs
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Diestel Graph Theory
Official site for Reinhard Diestel's Springer graduate text, where the main text is readable free online and paid eBook editions add the full apparatus. It covers matching, connectivity, planarity, colouring, flows, extremal theory, and minors.
Mathematics for Computer Science (MIT 6.042J)
Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs.
Graph Theory by Sarada Herke
Sixty-two short lectures building from definitions and isomorphism through trees, Eulerian and Hamiltonian graphs, planarity, colouring and matching, each proof worked step by step. A first pass before committing to a formal textbook.
Digraphs: Theory, Algorithms and Applications (free first edition)
The reference monograph on directed graphs: connectivity, tournaments, paths and cycles, flows in networks, orientations and hardness results, with algorithms throughout. Springer permits the corrected first edition to be downloaded free from Gutin's Royal Holloway page.
Graph Theory (Graduate Texts in Mathematics 173), 6th Edition
The standard modern reference, sixth edition 2025. Matching, connectivity, planarity, colouring, flows, extremal theory, Ramsey theory, random graphs and the minors theorem, with complete proofs. The author's site hosts a free online preview of the full main text.