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List of contents
Introduction to Graph Models
Graphs and Digraphs. Common Families of Graphs. Graph Modeling Applications. Walks and Distance. Paths, Cycles, and Trees. Vertex and Edge Attributes.
Structure and Representation
Graph Isomorphism. Automorphism and Symmetry. Subgraphs. Some Graph Operations. Tests for Non-Isomorphism. Matrix Representation. More Graph Operations.
Trees
Characterizations and Properties of Trees. Rooted Trees, Ordered Trees, and Binary Trees. Binary-Tree Traversals. Binary-Search Trees. Huffman Trees and Optimal Prefix Codes. Priority Trees. Counting Labeled Trees. Counting Binary Trees.
Spanning Trees
Tree Growing. Depth-First and Breadth-First Search. Minimum Spanning Trees and Shortest Paths. Applications of Depth-First Search. Cycles, Edge-Cuts, and Spanning Trees. Graphs and Vector Spaces. Matroids and the Greedy Algorithm.
Connectivity
Vertex and Edge-Connectivity. Constructing Reliable Networks. Max-Min Duality and Menger’s Theorems. Block Decompositions.
Optimal Graph Traversals
Eulerian Trails and Tours. DeBruijn Sequences and Postman Problems. Hamiltonian Paths and Cycles. Gray Codes and Traveling Salesman Problems.
Planarity and Kuratowski’s Theorem
Planar Drawings and Some Basic Surfaces. Subdivision and Homeomorphism. Extending Planar Drawings. Kuratowski’s Theorem. Algebraic Tests for Planairty. Planarity Algorithm. Crossing Numbers and Thickness.
Graph Colorings
Vertex-Colorings. Map-Colorings. Edge-Colorings. Factorization.
Special Digraph Models
Directed Paths and Mutual Reachability. Digraphs as Models for Relations. Tournaments. Project Scheduling. Finding the Strong Components of a Digraph.
Network Flows and Applications
Flows and Cuts in Networks. Solving the Maximum-Flow Problem. Flows and Connectivity. Matchings, Transversals, and Vertex Covers.
Graph Colorings and Symmetry
Automorphisms of Simple Graphs. Equivalence Classes of Colorings.
Appendix
Summary
Graph Theory and its Applications, Third Edition is the latest edition of the bestselling textbook for undergraduate courses in graph theory, yet expansive enough to be used for graduate courses. It takes a comprehensive, accessible approach to graph theory that integrates classical developments with emerging methods, models, and practical needs.
