Graph Theory

Contents

1. An Introduction to Graph

1. Introduction

2. Graph

2.1 Basic Terminologies and Properties of Graphs

2.2 Odd or Even Vertex

2.3 Graph Models

3. Special Types of Graphs and Basic Properties

4. Some Applications of Special Type of Graphs

4.1 Subgraph

4.2 Induced Subgraphs

5. Complement of a Graph

5.1 Self Complementary Graph

6. Union, Intersection and Product of Graphs

7. Fusion of Vertices

8. Isomorphism of Graphs

9. Matrix Representation of Graphs and Elementary Results  

2. Connected Graph

1. Introduction

2. Walk, Trail, Path, Cycle in Graph

3. Connected Graphs and Elementary Properties

3.1 Component

4. Some Definitions in Connected Graph

5. Isthmus and Cut Vertex

6. Connectivity

7. Weighted Graph and Dijkstra’s Algorithm

3. Euler and Hamilton Path

1. The Konigsberg Seven Bridge Problem

1.1 Eulerian Graph

2. Fleury’s Algorithm

3. Hamiltonian Graphs

3.1 Hamiltonian Circuit

3.2 Applications of Eulerian and Hamiltonian Graph

4. Trees

1. Definitions and Basic Terminologies

2. Properties and Applications of Trees

3. Centre of a Tree

4. Some Definitions in Connected Graph

5. Weighted Graph

6. Spanning Tree: Definition and Properties

7. Prim’s Algorithm

8. M-ary tree

9. Binary Tree

9.1 Definitions

9.2 Properties of Binary Trees

10. Tree Traversal