## Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ®Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics, provides an exciting new way to learn combinatorics and graph theory. With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Combinatorica. Three interesting classes of exercises are provided -- theorem/proof, programming exercises, and experimental explorations, providing great flexibility in teaching and learning the material.The Combinatorica user community ranges from students to engineers to researchers in mathematics, computer science, physics, economics, and the humanities. Combinatorica, which has received the EDUCOM Higher Education Software Award, is included with every copy of the popular computer algebra system Mathematica. |

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The Book Page: http://www.combinatorica.com/

### Contents

VIII | 1 |

IX | 3 |

X | 10 |

XI | 32 |

XII | 41 |

XIII | 53 |

XIV | 55 |

XV | 69 |

XXXVII | 226 |

XXXVIII | 229 |

XXXIX | 231 |

XL | 244 |

XLI | 258 |

XLII | 262 |

XLIII | 269 |

XLIV | 273 |

XVI | 76 |

XVII | 89 |

XVIII | 91 |

XIX | 93 |

XX | 104 |

XXI | 109 |

XXII | 131 |

XXIII | 133 |

XXIV | 135 |

XXV | 146 |

XXVI | 149 |

XXVII | 162 |

XXVIII | 173 |

XXIX | 177 |

XXX | 179 |

XXXI | 192 |

XXXII | 198 |

XXXIII | 200 |

XXXIV | 213 |

XXXV | 219 |

XXXVI | 224 |

XLV | 275 |

XLVI | 277 |

XLVII | 283 |

XLVIII | 294 |

XLIX | 306 |

L | 316 |

LI | 319 |

LII | 321 |

LIII | 323 |

LIV | 335 |

LV | 340 |

LVI | 343 |

LVII | 352 |

LVIII | 363 |

LIX | 370 |

LX | 372 |

LXI | 375 |

LXII | 376 |

LXIII | 447 |

LXIV | 459 |

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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 cube cycle index cycle structure default defined degree sequence deleted depth-first directed graph edge weights edges connecting EdgeStyle element enumeration Eulerian 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 labels length lexicographic order line graph matching Mathematica maximum minimum spanning tree multiple edges n-permutations necklaces NetworkFlow number of edges number of permutations number of vertices option pair of vertices partial order planar PlotRange problem random graphs rank recurrence representation returns RGFs self-loops set partitions SetGraphOptions shortest paths ShowGraph ShowGraph[g subgraph subset TableForm 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 |