Graph Theory An Introduction to Proofs, Algorithms, and Applications Textbooks in Mathematics Series
Auteur : Saoub Karin R
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.
Chapter 1: Graph Models, Terminology, and Proofs
Chapter 2: Graph Routes
Chapter 3: Trees
Chapter 4: Connectivity and Flow
Chapter 5: Matching and Factors
Chapter 6: Graph Coloring
Chapter 7: Planarity
Appendix
Selected Hints and Solutions
Dr. Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She received her PhD in Mathematics from Arizona State University and a Bachelor of Arts degree 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.
Date de parution : 03-2021
15.6x23.4 cm
Date de parution : 03-2021
15.6x23.4 cm
Thèmes de Graph Theory :
Mots-clés :
Hamiltonian Cycle; Graph theory; Eulerian Circuit; Hierholzer's algorithm; Bipartite Graph; Hamiltonian cycles; Chromatic Number; Graph terminology; Chinese Postman Problem; Eulerian circuits; Complete Graph; Augmenting Path; Vertex Cover; Augmenting Path Algorithm; Crossing Number; Hamiltonian Path; Interval Graphs; Minimum Vertex Cover; Score Sequence; Stable Matching; Kruskal's Algorithm; Edge Crossings; Planar Graph; Maximum Matching; Eulerian Trail; Odd Vertices; Induced Subgraph; Search Tree; Kuratowski’s Theorem; Odd Cycle