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# A-Level数学-图表与网络Graphs and Networks

A-Level 数学-图表与网络 Graphs and Networks
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

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