# D1

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tireni618's
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2015-06-08 16:23

## Section

Question | Answer |
---|---|

A graph | A graph G consists of points (vertices or nodes) which are connected by lines (edges or arcs). |

A subgraph | A subgraph of G is a graph, each of whose vertices belongs to G and each of whose edges belongs to G. |

A network | If a graph has a number associated with each edge (usually called its weight) then the graph is called a weighted graph or network |

A path | A path is a finite sequence of edges, such that the end vertex of one edge in the sequence is the start vertex of the next, and in which no vertex appears more than once. |

A walk | A walk is a path where you may visit vertices more than once. |

A cycle | A cycle (circuit) is a closed path, i.e. the end vertex of the last edge is the start vertex of the first edge. |

Two vertices are connected if | Two vertices are connected if there is a path between them. |

A connected graph | A graph is connected if all its vertices are connected. |

Diagraph | If the edges of a graph have a direction associated with them they are known as directed edges and the graph is known as a digraph. |

A tree | A tree is a connected graph with no cycles. |

A spanning tree | A spanning tree of a graph G is a subgraph which includes all the vertices of G and is also a tree. |

A minimum spanning tree | A minimum spanning tree (MST) is a spanning tree such that the total length of its arcs is as small as possible. (MST is sometimes called a minimum connector.) |

A complete graph | A graph in which each of the n vertices is connected to every other vertex is called a complete graph. |

A bipartite graph | A bipartite graph consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y, not vertices within a set. (If there are r vertices in X and s vertices in Y then this graph is Kr,s.) A bipartite graph has two sets of nodes. Nodes of one set can only be matched to nodes of the other set. |

A matching | A matching is the pairing of some or all of the elements of one set, X, with elements of a second set |

An alternating path | An Alternating Path starts at an unconnected vertex in one set and ends at an unconnected vertex in the other set |

The degree or valency | The degree or valency of a vertex is the number of edges incident to it. A vertex is odd (even) if it has odd (even) degree |

A complete matching | If every member of X is paired with a member of Y the matching is said to be a complete matching |