A First Course in Graph Theory 1st Edition by Gary Chartrand, Ping Zhang ISBN 978-0486483689 0486483681
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Product details:
ISBN 10: 0486483681
ISBN 13: 978-0486483689
Author: Gary Chartrand, Ping Zhang
This comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field’s most prominent experts, it takes an engaging approach that emphasizes graph theory’s history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications.
Optional sections designated as “excursion” and “exploration” present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols.
Table of contents:
1. Introduction
1.1. Graphs and Graph Models
1.2. Connected Graphs
1.3. Common Class of Gra
1.4. Multigraphs and Digraphs
2. Degrees
2.1. The Degree of a Vertex
2.2. Regular Graphs
2.3. Degree Sequences
2.4. Excursion: Graphs and Matrices
2.5. Exploration: Irregular Graphs
3. Isomorphic Graphs
3.1. The Definition of Isomorphi
3.2. bomorphism as a Relation
3.3. Excursion: Graphs and Groupe
3.4. Excursion: Reconstruction and Solvability
4. Trees
4.1. Bridges
4.2. Trees
4.3. The Minimum Spanning Tree Problem
4.4. Excursion: The Number of Spanning Trees
5. Connectivity
5.1. Cat-Vertin
5.2. Bucks
5.3. Connectivity
5.4. Menger’s Theorem
5.5. Exploration: Powers and Edge Labelings
6. Traversability
6.1. Ealerian Graphs
6.2. Hamiltonian Graphs
6.3. Exploration: Hamiltonian Walks
6.4. Excursion: Early Books of Graph Theory
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7. Digraphs
7.1. Strong Digraphs
7.2. Tournaments
7.3. Excursion: Decision Making
7.4. Exploration Wine Bottle Po
8. Matchings and Factorization
8.1. Matchings
8.2. Factorization
8.3. Decompositions and Graceful Labelings
8.4. Excursion Instant Insanity
8.5. Excursion: The Petersen Graph
8.6. Exploration: Bi-Graceful Graphs
9. Planarity
9.1. Planar Graphs
9.2. Embedding Graphs on Surfaces
9.3. Excursion: Thin Graphs
9.4. Exploration: Embedding Graphs in Graphs
10. Coloring Graphs
10.1. The Four Color Problem
10.2. Vertex Coloring
10.3. Edge Coloring
10.4. Excursion: The Heawood Map Coloring Theorem
10.5. Exploration: Modular Coloring
11. Ramsey Numbers
11.1. The Ramsey Number of Graph
11.2. T’s Theorem
11.3. Exploration: Modified Ramsey Numbers
11.4. Excuck Numbers
12. Distance
12.1. The Center of a Graph
12.2. Rich Vertices
12.3. Excursion: Locating Numbers
12.4. Excursion Detour and Directed Distance
12.5. Exploration: Channel Asset
12.6. Exploration: Distance Between Graphs
13. Domination
13.1. The Domination Number of a Graph
13.2. Exploration: Stratification
13.3. Exploration: Lights Out
13.4. Excursion And Still It Go More Colorful
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Tags: Gary Chartrand, Ping Zhang, A First Course, Graph Theory