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### Contents

GRAPHS | 12 |

Introduction Sets Paradox Graphs Graph | 31 |

Recognizing Isomorphic Graphs Semantics | 56 |

Copyright | |

2 other sections not shown

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### Common terms and phrases

1-platonic algebraic Chapter chromatic number closed euler walk closed hamilton walk complete graph connected graph Corollary crossing-free drawing cyclic graph Definition denoted drawn in Figure drawn without edge-crossings edge set edges of G element empty set equal erasing Euclidean geometry Euler's Formula example Exercise expansion of UG Five Color Theorem Four Color Conjecture G is planar graph G graph of Figure graph theory intuition isomorphic graphs joined Jordan Curve Theorem K5 is nonplanar Kuratowski's Theorem Lemma Let G mathematical induction mathematicians multigraph nonplanar graphs null graph number of edges number of vertices odd number odd vertices open euler walk planar and connected planar graph plane without edge-crossings platonic graph polygonal graph positive integer problem proof prove pure mathematics regular of degree second graph six vertices statement subgraph supergraph of UG surface topology true UG and K5 UG or K5 vertex set vertices of degree