## Handbook of Graph TheoryThe 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

INTRODUCTION to GRAPHS | 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

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

### Popular passages

Page 57 - (V, E) consists of a finite, nonempty set of vertices V and a set of edges E. Each edge is a