Introduction to Graph Theory H3 Mathematics 1st edition by Koh Khee Meng, Dong Fengming, Tay Eng Guan ISBN 9812703861 978-9812703866

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ISBN 10: 9812703861
ISBN 13: 978-9812703866
Author: Koh Khee Meng, Dong Fengming, Tay Eng Guan

 Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

Introduction to Graph Theory H3 Mathematics 1st Table of contents:

1 . Fundamental Concepts and Basic Results

1.1 The Konigsberg bridge problem

1.2 Multigraphs and graphs

Exercise 1.2

1.3 Vertex degrees

Exercise 1.3

1.4 Paths, cycles and connectedness

Exercise 1.4

2 . Graph Isomorphisms, Subgraphs, the Complement of a Graph

2.1 Isomorphic graphs and isomorphisms

2.2 Testing isomorphic graphs

Exercise 2.2

2.3 Subgraphs of a graph

Exercise 2.3

2.4 The complement of a graph

Exercise 2.4

3 . Bipartite Graphs and Trees

3.1 Bipartite graphs

Exercise 3.1

3.2 Trees

Exercise 3.2

3.3 (*) Spanning trees of a graph

Exercise 3.3

4 . Vertex-colourings of Graphs

4.1 The four-colour problem

4.2 Vertex-colourings and chromatic number

Exercise 4.2

4.3 Enumeration of chromatic number

Exercise 4.3

4.4 Greedy colouring algorithm

Exercise 4.4

4.5 An upper bound for the chromatic number and Brooks’ theorem

Exercise 4.5

4.6 Applications

Exam Timetable

Chemical Storage

Exercise 4.6

5 . Matchings in Bipartite Graphs

5.1 Introduction

5.2 Matchings

Exercise 5.2

5.3 Hall’s theorem

Exercise 5.3

5.4 System of distinct representatives

Exercise 5.4

6 . Eulerian Multigraphs and Hamiltonian Graphs

6.1 Eulerian multigraphs

Exercise 6.1

6.2 Characterization of Eulerian multigraphs

Exercise 6.2

6.3 Around the world and Hamiltonian graphs

6.4 A necessary condition for a graph to be Hamiltonian

Exercise 6.4

6.5 Two sufficient conditions for a graph to be Hamiltonian

Exercise 6.5

7 . Digraphs and Tournaments

7.1 Digraphs

Exercise 7.1

7.2 Basic concepts

The in-degree and out-degree of a vertex

Isomorphic digraphs

Connectedness

Exercise 7.2

7.3 Tournaments

Transitive tournaments

Exercise 7.3

7.4 Two properties of tournaments

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Tags: Koh Khee Meng, Dong Fengming, Tay Eng Guan, Graph Theory, H3 Mathematics