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Networks, SMB-007

The city of Robville contains eight landmarks denoted as vertices `N` to `U` on the network diagram below. The edges on this network represent the roads that link the eight landmarks.
 

  

  1. Write down the degree of vertex `U`.  (1 mark)

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  2. Steven wants to visit each landmark, but drive along each road only once. He will begin his journey at landmark `N`.
  3. At which landmark must he finish his journey?  (1 mark)

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  4. Regardless of which route Steven decides to take, how many of the landmarks (including those at the start and finish) will he see on exactly two occasions?  (2 marks)

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Show Answers Only
  1. `4`
  2. `P\ text{(the other odd degree vertex)}`
  3. `5`
Show Worked Solution

i.   `4`
 

ii.   `P\ text{(the other odd degree vertex)}`

`text{(The Konigsberg Bridge concept is used here)}`
 

iii.   `text{Any vertex (landmark) with a degree of 3 or 4 will be seen twice.}`

`5 (N, T, R, P, U)`

Filed Under: Trails, Paths and Cycles Tagged With: num-title-ct-path, smc-4789-50-Eulerian trails, smc-4789-70-Konigsberg

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