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Question 1
A transport network connects five distribution centres, labelled A, B, C, D, and E. The network is shown in the diagram below.
(a) Define planar graph. (1 mark)
(b) The network has been redrawn as a planar graph in the diagram. How many faces does this planar graph have? (1 mark)
(c) The network has 5 vertices and 7 edges. Use Euler's formula \( V - E + F = 2 \) to verify the number of faces you stated in part (b). Show your working. (2 marks)
(d) State the degree sequence of the planar graph. (1 mark)
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Question 2
Which of the following statements best describes what makes a graph planar?
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Question 3
The planar graph shown has vertices A, B, C, D, E and F.
(a) Define **planar graph**. (1 mark)
(b) State the number of edges in the graph. (1 mark)
(c) Determine the number of faces in the graph. (1 mark)
(d) Use Euler's formula \( V - E + F = 2 \) to verify your answer to part (c). (1 mark)
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Question 4
Which of the following graphs correctly represents a planar graph?
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