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Graph Theory by Keijo Ruohonen
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About this book :-
Graph Theory written by
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
Author(s): Keijo Ruohonen
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Book Contents :-
Graph Theory written by
cover the following topics.
1. DEFINITIONS AND FUNDAMENTAL CONCEPTS
1.2 Walks, Trails, Paths, Circuits, Connectivity, Components
1.3 Graph Operations
1.5 Labeled Graphs and Isomorphism
2.1 Trees and Forests
2.2 (Fundamental) Circuits and (Fundamental) Cut Sets
3. DIRECTED GRAPHS
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
7.1 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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