Networks, SMB-005

The vertices in the network diagram below show the entrance to a wildlife park and six picnic areas in the park: `P1`, `P2`, `P3`, `P4`, `P5` and `P6`.

The numbers on the edges represent the lengths, in metres, of the roads joining these locations.

In this graph, what is the degree of the vertex at the entrance to the wildlife park? (1 mark)

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What is the shortest distance, in metres, from the entrance to picnic area `P3`? (1 mark)

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A park ranger starts at the entrance and drives along every road in the park once.

At which picnic area will the park ranger finish? (2 marks)

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What mathematical term is used to describe the route the park ranger takes? (1 mark)

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Show Answers Only

`3`
`1000\ text(m)`
`P4`
`text(Euler trail)`

Show Worked Solution

i. `3`

ii. `text( Shortest distance)`

`= E-P1-P3`

`= 600 + 400`

`= 1000\ text(m)`

iii. `text(A route could be)`

`E − P1 − P2 − P3 − P4 − P5`

`− E − P6 − P1 − P3 − P6 − P4`

`:.\ text(Finish at)\ P4`

`text{(Konigsberg bridge – Eulerian trail ends at the only other}`

`text{odd degree vertex)}`

iv. `text(Eulerian trail)`