## Handbook of Graph Theory (Google eBook)The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as "pure" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference. Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to find and easy to understand. The treatment of each topic includes lists of essential definitions and facts accompanied by examples, tables, remarks, and in some areas, conjectures and open problems. Each section contains a glossary of terms relevant to that topic and an extensive bibliography of references that collectively form an extensive guide to the primary research literature. The applications of graph theory are fast becoming ubiquitous. Whether your primary area of interest lies in mathematics, computer science, engineering, or operations research, this handbook holds the key to unlocking graph theory's intricacies, applications, and potential. |

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### Contents

1 | |

2 | |

20 | |

29 | |

Glossary | 50 |

GRAPH REPRESENTATION | 56 |

57 | |

68 | |

574 | |

Glossary | 599 |

TOPOLOGICAL GRAPH THEORY | 610 |

611 | |

625 | |

642 | |

661 | |

684 | |

79 | |

99 | |

Glossary | 119 |

DIRECTED GRAPHS | 126 |

127 | |

142 | |

156 | |

Glossary | 185 |

CONNECTIVITY and TRAVERSABILITY | 193 |

194 | |

214 | |

237 | |

253 | |

261 | |

279 | |

300 | |

Glossary | 330 |

COLORINGS and RELATED TOPICS | 340 |

341 | |

365 | |

389 | |

403 | |

431 | |

445 | |

Glossary | 475 |

ALGEBRAIC GRAPH THEORY | 484 |

485 | |

505 | |

516 | |

533 | |

557 | |

696 | |

722 | |

737 | |

761 | |

Glossary | 770 |

ANALYTIC GRAPH THEORY | 787 |

788 | |

817 | |

837 | |

860 | |

Glossary | 868 |

GRAPHICAL MEASUREMENT | 872 |

873 | |

889 | |

910 | |

922 | |

Glossary | 945 |

GRAPHS in COMPUTER SCIENCE | 952 |

953 | |

985 | |

1015 | |

1046 | |

Glossary | 1067 |

NETWORKS and FLOWS | 1074 |

1075 | |

1087 | |

1103 | |

1117 | |

Glossary | 1139 |

1143 | |

### Common terms and phrases

1-factor 2-connected adjacency matrix algorithm automorphism bipartite graph Cayley graph chromatic number circuit clique closed surface coloring Combin Combinatorial complete graph components Comput conjecture connected graph contains cutset decomposition DEFINITIONS deletion denoted digraph digraph G directed graph Discrete Math edge-connectivity edge-reconstructible edges of G eigenvalues Erdos eulerian tour EXAMPLE exists FACTS Figure finite given graph drawing graph G graph imbedding graph of order Graph Theory hamiltonian cycle heuristics hypergraph independent set induced subgraph integer interval graph isomorphic labeled least Let G linear matroid maximal maximum genus minimal minimum degree NOTATION number of edges number of vertices orientable partition permutation planar graph polynomial problem Proc Ramsey numbers random graph reconstruction regular graphs REMARKS rooted tree sequence shortest paths simple graph spanning tree subset symmetric theorem timetabling topological torus tournament transitive triangulation undirected vector vertex vertex set vertex-transitive voltage graph