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Networks, SMB-008

The diagram below shows a network of train lines between five towns: Attard, Bower, Clement, Derrin and Eden.

The numbers indicate the distances, in kilometres, that are travelled by train between connected towns.
 

 

Charlie followed an Eulerian trail through this network of train lines.

  1. Write down the names of the towns at the start and at the end of Charlie’s trail.  (1 mark)

    --- 2 WORK AREA LINES (style=lined) ---

  2. What distance did he travel?  (2 marks)

    --- 3 WORK AREA LINES (style=lined) ---

Show Answers Only
  1. `text(Bower, Eden)`
  2. `910\ text(km)`
Show Worked Solution

i.   `text{Eulerian trail starts and ends at odd degree vertices (towns).}`

`text(Bower, Eden or Eden, Bower)`

 
ii.
   `text{Eulerian trail}\ =>\ text{every edge used once only.}`

`text{Distance}\ (BDABCDEACE)`

`= 160 + 130 + 80 + 70 + 60 + 40 + 100 + 150 + 120`

`= 910\ text(km)`

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

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