Discrete%20Maths

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Discrete Maths

• Chapter 2 Graphs and Networks
• Lesson 2 Hello Mr Euler

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Where graph theory came from
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Where graph theory came from
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(No Transcript)
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Lets learn some definitions
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Trail (or route)
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Closed Trail
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Path
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Cycle
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Order
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Connected Graph
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Eulerian Graph

• A connected graph which has a closed trail
  containing every arc precisely once

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• CHECK A connected graph is Eulerian if and only
  if every node has an even order

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A wee puzzle
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Semi-Eulerian Graph

• A graph which has a trail that is not closed that
  contains every arc precisely once

• CHECK A connected graph is Semi-Eulerian if and
  only if precisely two nodes have odd order