1. Introductory Concepts
Mathematical Preliminaries / Mathematical Induction / Permutations and Combinations / Pascal's Triangle and Combinatorial Identities
2. Introduction to Graphs and Their Uses
Graphs as Models / Subgraphs and Types of Graphs / Isomorphic Graphs / Graph Operations
3. Trees and Bipartite Graphs
Properties of Trees / Minimum Spanning Trees / A Characterization of Bipartite Graphs / Matchings and Job Assignments
4. Distance and Connectivity
Distance in Graphs / Connectivity Concepts / Applications
5. Eulerian and Hamiltonian Graphs
Characterization of Eulerian Graphs / Hamiltonicity / Applications
6. Graph Coloring
Vertex Coloring and Independent Sets / Edge Coloring / Applications of Graph Coloring
7. Matrices
Review of Matrix Concepts / The Adjacency Matrix / The Distance Matrix
8. Graph Algorithms
Graph Searching / Graph Coloring Algorithms / Tree Codes
9. Planar Graphs
Planarity / Planar Graphs, Graph Coloring, and Embedding / Graph Duals and a Planar Graph Application
10. Digraphs and Networks
Directed Graphs / Networks / The Critical Path Method
11. Special Topics
Ramsey Theory / Domination in Graphs
Answers/Solutions to Selected Exercises
365 pages, $73.95 list
1-4786-1175-8
978-1-4786-1175-2
© 2003
paperback
eBook availability
Introductory Graph Theory with Applications
Graph theory’s practical applications extend not only across multiple areas of mathematics and computer science but also throughout the social sciences, business, engineering, and other subjects. Buckley and Lewinter have written their text with students of all these disciplines in mind. Pedagogically rich, the authors provide hundreds of worked-out examples, figures, and exercises of varying degrees of difficulty.
Concepts are presented in a readable and accessible manner, and applications are stressed throughout so the reader never loses sight of the powerful tools graph theory provides to solve real-world problems. Such diverse areas as job assignment, delivery truck routing, location of emergency or service facilities, network reliability, zoo design, exam scheduling, error-correcting codes, facility layout, and the critical path method are covered.
Concepts are presented in a readable and accessible manner, and applications are stressed throughout so the reader never loses sight of the powerful tools graph theory provides to solve real-world problems. Such diverse areas as job assignment, delivery truck routing, location of emergency or service facilities, network reliability, zoo design, exam scheduling, error-correcting codes, facility layout, and the critical path method are covered.