## Graph Theory |

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### Contents

Discrete Numeric Functions and Generating Functions 3658 | 36 |

Recurrence Relations 5989 | 59 |

11 | 81 |

12 | 88 |

Graphs 901 1 7 | 90 |

13 | 100 |

Euler and Hamiltonian Graphs 1 1 81 39 | 118 |

Trees 1401 64 | 140 |

Planar and Dual Graphs 183205 | 183 |

Vector Spaces of a Graph 206_219 | 206 |

Matrixrepresentation of Graphs 220240 | 220 |

Applications of Graph Theory 297300 | 297 |

### Common terms and phrases

adjacency matrix algorithm binary tree called chromatic polynomial complete graph components connected graph contains corresponding cycle defined denoted digits digraph directed graph disjoint edge connectivity edge in G edge-connectivity edge-disjoint edges incident edges of G elements Euler circuit Euler graph Euler path Eulerian EXAMPLE FIGURE ﬂow fundamental circuits G and G G1 and G2 geometric dual given graph given recurrence relation graph G Hamiltonian circuit Hamiltonian path Hence incidence matrix indegree inorder integers internal vertex isomorphic kuratowski Let G maximal modulo node null graph number of edges number of vertices numeric function odd degree pair of vertices parallel edges permutation planar graph plane problem Proof proper coloring real number recurrence relation region ring sum rooted tree simple graph Solve the recurrence spanning tree subgraph of G subset subspace Suppose THEOREM total number traversal vector space vertex set vertices of degree vertices of G vertices of odd zero