## Topological Graph TheoryThis definitive treatment written by well-known experts emphasizes graph imbedding while providing thorough coverage of the connections between topological graph theory and other areas of mathematics: spaces, finite groups, combinatorial algorithms, graphical enumeration, and block design. Almost every result of studies in this field is covered, including most proofs and methods. Its numerous examples and clear presentation simplify conceptually difficult material, making the text accessible to students as well as researchers. Includes an extensive list of references to current literature. |

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### Contents

graph homeomorphisms | 17 |

VOLTAGE GRAPHS AND COVERING SPACES | 56 |

SURFACES AND GRAPH IMBEDDINGS | 95 |

Copyright | |

9 other sections not shown

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### Common terms and phrases

action acts adjacent automorphism band base graph boundary walk bouquet branch points branched covering called Cayley graph circles color complete graph component compute connected Consider construction contains contraction Corollary corresponding covering current graph cycle cyclic defined denoted derived graph derived imbedding direction Draw dual edge element endpoints equal equation equivalent Euler characteristic Example Exercise faces Figure finite fixed follows four genus given gives graph G graph imbedding homeomorphic identified illustrated imbedded voltage graph imbedding G implies isomorphic labeled Let G loop natural nonorientable obtained ordinary orientable original permutation voltage planar plane possible presentation problem projection Proof Prove quadrilateral quotient reflection region regular relator respectively resulting rotation rotation system shows sides simplicial space space group sphere subgraph subgroup Suppose surface symmetric Theorem Theory topological torus tree triangle valence vertex vertices voltage graph yields