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Algorithmic Graph Theory Book

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Algorithmic Graph Theory David Joyner, Minh Van Nguyen, Nathann Cohen Version 0.3 Copyright c 2009–2010 David Joyner Minh Van Nguyen Nathann Cohen Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License”. Edition Version 0.3 19 March 2010 Contents Acknowledgements iii List of Algorithms v List of Figures vii List of Tables ix 1 Introduction to Graph Theory 1.1 Graphs and digraphs . . . . . . . . 1.2 Subgraphs and other graph types . 1.3 Representing graphs using matrices 1.4 Isomorphic graphs . . . . . . . . . 1.5 New graphs from old . . . . . . . . 1.6 Common applications . . . . . . . . . . . . . . 1 1 5 10 14 18 23 2 Graph Algorithms 2.1 Graph searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Shortest path algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 25 28 3 Trees and Forests 3.1 Properties of trees . . . . . . . . . 3.2 Minimum spanning trees . . . . . 3.3 Binary trees . . . . . . . . . . . . 3.4 Applications to computer science . . . . 37 38 40 48 57 . . . . 61 61 61 61 62 . . . . 63 63 63 63 64 4 Distance and Connect ...
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