您现在的位置:52Alevel学习网 > 学习资料 > 课程辅导 >

A-Level数学-图表与网络Graphs and Networks

2018-03-10 16:44http://www.52alevel.com52Alevel学习网

  Revision: Graphs and Networks

  Definitions

  In a complete graph every node is connected by an arc to each of the other nodes. There are 1/2*n (n-1) arcs in a complete graph with n nodes.

  In a connected graph there are no isolated nodes.

  A trail is a sequence of arcs such that the end node of one arc is the start node of the next.

  A closed trail (or cycle) is a route through the nodes which starts and finishes in the same place. No arc is used more than once. Only the start node is used more than once.

  A path is a trail where no node is passed more than once.

  The order of a node is the number of arcs meeting at that node.

  An Eulerian graph is a connected graph which has a closed trail containing every arc precisely once. This can occur if and only if every node is even.

  A semi-Eulerian graph is a connected graph which has a trail (not closed) containing every arc precisely once. It occurs when a graph has 2 odd nodes: the trail starts at one odd node and ends at the other.

  A planar graph is one which can be drawn so that arcs do not cross each other.

  Matrix formulation

  Networks can be represented by matrices. If the network has only 2 way links (no arrows) the matrix is symmetrical about a diagonal drawn from top left to bottom right.

 

工商标识