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. Table of Contents:
1. Introductory Concepts 2. Introduction to Graphs and Their Uses 3. Trees and Bipartite Graphs 4. Distance and Connectivity 5. Eulerian and Hamiltonian Graphs 6. Graph Coloring 7. Matrices 8. Graph Algorithms 9. Planar Graphs 10. Digraphs and Networks 11. Special Topics Answers/Solutions to Selected Exercises
Title of related interest also from Waveland Press: Molluzzo-Buckley, A First Course in Discrete Mathematics (ISBN 9780881339406).
Author(s): Fred Buckley, Marty Lewinter
Edition: 1
Publisher: Waveland Press, Inc.
Year: 2013
Language: English
Pages: 365
Contents
Preface
Notation
1. Introductory Concepts
1.1 Mathematical Preliminaries
1.2 Mathematical Induction
1.3 Permutations and Combinations
1.4 Pascal's Triangle and Combinatorial Identities
2. Introduction to Graphs and Their Uses
2.1 Graphs as Models
2.2 Subgraphs and Types of Graphs
2.3 Isomorphic Graphs
2.4 Graph Operations
3. Trees and Bipartite Graphs
3.1 Properties of Trees
3.2 Minimum Spanning Trees
3.3 A Characterization of Bipartite Graphs
3.4 Matchings and Job Assignments
4. Distance and Connectivity
4.1 Distance in Graphs
4.2 Connectivity Concepts
4.3 Applications
5. Eulerian and Hamiltonian Graphs
5.1 Characterization of Eulerian Graphs
5.2 Hamiltonicity
5.3 Applications
6. Graph Coloring
6.1 Vertex Coloring and Independent Sets
6.2 Edge Coloring
6.3 Applications of Graph Coloring
7. Matrices
7.1 Review of Matrix Concepts
7.2 The Adjacency Matrix
7.3 The Distance Matrix
8. Graph Algorithms
8.1 Graph Searching
8.2 Graph Coloring Algorithms
8.3 Tree Codes
9. Planar Graphs
9.1 Planarity
9.2 Planar Graphs, Graph Coloring, and Embedding
9.3 Graph Duals and a Planar Graph Application
10. Digraphs and Networks
10.1 Directed Graphs
10.2 Networks
10.3 The Critical Path Method
11. Special Topics
11.1 Ramsey Theory
11.2 Domination in Graphs
Answers/Solutions to Selected Exercises
Index
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