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Graph Theory by Keijo Ruohonen
**

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**About this book :- **
**Graph Theory ** written by
** Keijo Ruohonen**.

This book contain an introduction to basic concepts and results in graph theory, with a special emphasis put on
the network-theoretic circuit-cut dualism.
One of the usages of graph theory is to give a unified formalism for many very differentlooking
problems. It then suffices to present algorithms in this common formalism. This has
lead to the birth of a special class of algorithms, the so-called graph algorithms. Half of the
text of these notes deals with graph algorithms, again putting emphasis on network-theoretic
methods. Only basic algorithms, applicable to problems of moderate size, are treated here.
Special classes of algorithms, such as those dealing with sparse large graphs, ”small-world”
graphs, or parallel algorithms will not be treated.

**Book Detail :- **
** Title: ** Graph Theory
** Edition: **
** Author(s): ** Keijo Ruohonen
** Publisher: **
** Series: **
** Year: ** 2008
** Pages: ** 114
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: **
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**Book Contents :- **
**Graph Theory ** written by
** Keijo Ruohonen**
cover the following topics.
**1. DEFINITIONS AND FUNDAMENTAL CONCEPTS**

1.1 Definitions

1.2 Walks, Trails, Paths, Circuits, Connectivity, Components

1.3 Graph Operations

1.4 Cuts

1.5 Labeled Graphs and Isomorphism
**2. TREES**

2.1 Trees and Forests

2.2 (Fundamental) Circuits and (Fundamental) Cut Sets
**3. DIRECTED GRAPHS**

3.1 Definition

3.2 Directed Trees

3.3 Acyclic Directed Graphs
**4. MATRICES AND VECTOR SPACES OF GRAPHS**

4.1 Matrix Representation of Graphs

4.2 Cut Matrix

4.3 Circuit Matrix

4.4 An Application: Stationary Linear Networks

4.5 Matrices over GF(2) and Vector Spaces of Graphs
**5. GRAPH ALGORITHMS**

5.1 Computational Complexity of Algorithms

5.2 Reachability: Warshall’s Algorithm

5.3 Depth-First and Breadth-First Searches

5.4 The Lightest Path: Dijkstra’s Algorithm

5.5 The Lightest Path: Floyd’s Algorithm

5.6 The Lightest Spanning Tree: Kruskal’s and Prim’s Algorithms

5.7 The Lightest Hamiltonian Circuit (Travelling Salesman’s Problem): The Annealing Algorithm and the Karp–Held Heuristics

5.8 Maximum Matching in Bipartite Graphs: The Hungarian Algorithm

5.9 Maximum Flow in a Transport Network: The Ford–Fulkerson Algorithm
**6. DRAWING GRAPHS**

6.1 Planarity and Planar Embedding

6.2 The Davidson–Harel Algorithm
**7. MATROIDS**

7.1 Hereditary Systems

7.2 The Circuit Matroid of a Graph

7.3 Other Basic Matroids

7.4 Greedy Algorithm

7.5 The General Matroid

7.6 Operations on Matroids

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**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

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