## Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ®This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains. |

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### Contents

VIII | xiv |

IX | xiv |

X | 10 |

XI | 32 |

XII | 41 |

XIII | 53 |

XIV | 55 |

XV | 69 |

XXXVII | 224 |

XXXVIII | 227 |

XXXIX | 229 |

XL | 242 |

XLI | 256 |

XLII | 260 |

XLIII | 267 |

XLIV | 271 |

XVI | 76 |

XVII | 87 |

XVIII | 89 |

XIX | 91 |

XX | 102 |

XXI | 107 |

XXII | 129 |

XXIII | 131 |

XXIV | 133 |

XXV | 144 |

XXVI | 147 |

XXVII | 160 |

XXVIII | 171 |

XXIX | 175 |

XXX | 177 |

XXXI | 190 |

XXXII | 196 |

XXXIII | 198 |

XXXIV | 211 |

XXXV | 217 |

XXXVI | 222 |

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### Common terms and phrases

adjacency matrix algorithm automorphism biconnected bijection bipartite graph breadth-first Bruijn circulant graphs clique colors Combinatorica functions complete graph compute connected components constructs corresponding cycle index cycle structure default defined degree sequence deleted depth-first directed graph edge weights edges connecting EdgeStyle element enumeration Eulerian exactly example False fc-subsets FiniteGraphs gives graph data structure graph g graph theory GraphOptions Gray code Gray code order grid graph Hamiltonian cycle Hamiltonian path hypercube identical implementation Infinity integer partitions involutions isomorphic k-subset labels length lexicographic order line graph matching maximum minimum spanning tree multiple edges n-permutations necklaces network flow number of edges number of permutations number of vertices option pair of vertices partial order planar PlotRange problem random graphs rank recurrence returns RGFs self-loops set partitions SetGraphOptions shortest paths ShowGraph ShowGraph[g subgraph subsets takes transposition graph Type undirected unranking vertex cover VertexColor VertexLabel VertexNumber VertexStyle WeightingFunction yields True Young tableaux

### References to this book

Discrete Algorithmic Mathematics, Third Edition Stephen B. Maurer,Anthony Ralston No preview available - 2005 |