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Graph Theory by Keijo Ruohonen

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Graph Theory written by Keijo Ruohonen . This is an other great mathematics book 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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