Graph Theory: An Introduction to Proofs, Algorithms, and Applications
Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis.
This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results. Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations.
Current applications and exploratory exercises are provided to further the reader’s mathematical reasoning and understanding of the relevance of graph theory to the modern world.
Features
The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book
The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths.
The third chapter focuses entirely on trees – terminology, applications, and theory.
Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach.
Hints and Solutions to selected exercises provided at the back of the book.
Author
Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She earned her PhD in mathematics from Arizona State University and BA from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.
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Introduction to Graph Theory
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Introduction to Graph Theory
+作者：Malik
+年份：2014 年1 版
+ISBN：9789814416931
+書號：MA0361P
+規格：平裝/單色
+頁數：512
+出版商：Cengage
•Learning Objectives offer an outline of the concepts discussed in detail in the chapter.
•Some Key Definitions and Some Key Highlights at the end of each chapter reinforce students’ understanding of the key concepts learnt.
•Exercises further reinforce learning and ensure that students have, in fact, learned the concepts presented in each chapter.
•Programming Exercises allow students to apply their coding skills in C++ and Java using the concepts learnt in the chapter.
•Remarks highlight important facts about the concepts introduced in the chapter.
•More than 400 visual diagrams, both extensive and exhaustive, illustrate difficult concepts.
•Numbered Examples illustrate the key concepts.
•Worked-Out Exercises is a set of fully worked-out exercises provided at the end of each chapter.
1. Basic Properties of Graphs
2. Connectivity and Bipartite Graphs
3. Eulerian Graphs and Hamiltonian Graphs
4. Matrix Representation and Isomorphisms of Graphs
5. Graph Algorithms
6. Trees
7. Rooted Trees
8. Spanning Trees
9. Planar Graphs and Graph Coloring
10. Networks
11. Interval Graphs
12. Intersection Graphs
Appendix A—A Review of Basic Set Theory and Algorithms
Appendix B—Answers and Hints to Selected Exercises References Index
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