The Citizens of the Scandinavian Town of Gamsholm - Management Assignment Help

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Assignment Task

 

1. The citizens of the Scandinavian town of Gamsholm are trying to solve a puzzle: is It possible to take a wundenur, that is, a cycle ride through Gamsholm that crosses each of its seven bridges exactly once? (Note that a wundertur does not have to start and end at the same point). 

(a) Turn this map of Gamsholm Into a graph, and find Its degree sequence. Is this graph simple?

(b) Explain why there can be no wundertur through Garrisholm. (You can assume any results we proved In the lectures, but you should state what they are.)

(c) The citizens of South Island are so annoyed by your argument that they decide to demolish one of the three bridges connecting them to the rest of Gamsholm. Indicate on your graph which of the bridges they could choose to remove If they want to make it possible to take a wundertur. Give a brieflusfificatIon.

2. A simple connected graph C has ten vertices of degree 7 and one of degree 6, and no other vertices.

(a) Now many edges does It have? Be sure to state clearly any results that you use to get your answer.

(b) If this graph had a planar drawing, how many faces would it have? Be sure to state clearly any results that you use to get your answer.

(c) Explain why it follows that C cannot be planar. 
 

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