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Networks, SMB-001

The network diagram below describes a skateboard park with seven ramps.

The ramps are shown as vertices `T`, `U`, `V`, `W`, `X`, `Y` and `Z` on the graph below.
 

 

The tracks between ramps `U` and `V` and between ramps `W` and `X` are rough, and cannot be used by skateboards.

  1. Describe a path that a skateboarder at ramp `V` could use to travel to ramp `T` that uses 4 edges only.   (1 mark)

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

  2. A skateboarder begins skating at ramp `W` and follows an Eulerian trail.
  3. What trail does the skateboarder take?  (2 marks)

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

Show Answers Only
  1. `text{Possible paths:}\ \ VZYT, VZUT`
  2. `XYZWVZUYTU\ \ \text{(Finishes at ramp}\ U\text{)}`
Show Worked Solution

i.    `text{Possible paths:}\ \ VZYT, VZUT, VZYUT`

 
ii.
    `text{The Eulerian trail (visits each edge exactly once):}`

`XYZWVZUYTU`

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

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