## Introductory Discrete MathematicsThis overview of discrete mathematics places special emphasis on combinatorics, graph theory and two important topics in network optimization with an algorithmic approach. The text provides a discussion of basic combinatorics and graph theory, with several combinational models. |

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### Contents

Combinatorics | 35 |

Generating Functions | 80 |

Recurrence Relations | 94 |

Copyright | |

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### Common terms and phrases

adjacency matrix algorithm to solve allocating arbitrary binary tree bipartite graph called cardinality Chapter coefficient color complexity compound proposition connected graph consider cutset decision problem defined delete denoted digraph directed Hamiltonian path distinct objects empty set equal equivalence relation Eulerian circuit Eulerian path exactly Example Figure Find the number finite set graph G Hamiltonian cycle Hamiltonian path indegree initial conditions intersection Iteration least letters linear marbles mathematics maximal element N(A ſl natural numbers nonnegative integers NP-complete number of edges number of elements number of multiplications number of solutions number of vertices obtain optimization problem ordinary generating function outdegree pair of vertices partially ordered set partition permutations pigeonhole polynomial algorithm positive integers Proof Prove r-collection real numbers recurrence relation represent root sequence simple graph solutions in nonnegative spanning tree subgraph Suppose surjection THEOREM total number tournament true unique variable vertex weight word