A local charity has set up a carnival for small children in a park with existing walkways and they need to create a map and advertising campaign. (a) Draw a simple graph that models the walkways and attractions of the carnival given the following information: • the entrance is an attraction because of the funny clowns that perform • from the clowns you can go to the slide, food truck, or carousel • the food truck is also connected to the petting zoo, ice cream cart, and ring toss • you can get to the petting zoo from the slide as well • from the carousel you can go to the face painting station or the ice cream cart, but there is also a direct path between the ice cream cart and face painting station too • the ice cream cart and ring toss both lead to the fishing game (b) To advertise the event, (i) Can the charity claim each attraction can be visited exactly once? (e.g. does the graph have a Hamilton circuit? or a Hamilton path?) If so, give one example, as proof. (ii) For members of the population that always walk through this park, • can the charity claim that the locals are still able to travel along each walkway exactly once and exit the carnival? (e.g. does the graph have an Euler circuit?) Prove your answer. • can the charity claim that the locals are still able to walk along each walkway within the carnival exactly once? (e.g. does the graph have an Euler path?) Prove your answer.

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A local charity has set up a carnival for small children in a park with existing walkways and they need to create a
map and advertising campaign.
(a) Draw a simple graph that models the walkways and attractions of the carnival given the following information:
• the entrance is an attraction because of the funny clowns that perform
• from the clowns you can go to the slide, food truck, or carousel
• the food truck is also connected to the petting zoo, ice cream cart, and ring toss
• you can get to the petting zoo from the slide as well
• from the carousel you can go to the face painting station or the ice cream cart, but there is also a direct path
between the ice cream cart and face painting station too
• the ice cream cart and ring toss both lead to the fishing game
(b) To advertise the event,
(i) Can the charity claim each attraction can be visited exactly once? (e.g. does the graph have a Hamilton circuit?
or a Hamilton path?) If so, give one example, as proof.
(ii) For members of the population that always walk through this park,
• can the charity claim that the locals are still able to travel along each walkway exactly once and exit the
carnival? (e.g. does the graph have an Euler circuit?) Prove your answer.
• can the charity claim that the locals are still able to walk along each walkway within the carnival exactly once?
(e.g. does the graph have an Euler path?) Prove your answer.
Transcribed Image Text:A local charity has set up a carnival for small children in a park with existing walkways and they need to create a map and advertising campaign. (a) Draw a simple graph that models the walkways and attractions of the carnival given the following information: • the entrance is an attraction because of the funny clowns that perform • from the clowns you can go to the slide, food truck, or carousel • the food truck is also connected to the petting zoo, ice cream cart, and ring toss • you can get to the petting zoo from the slide as well • from the carousel you can go to the face painting station or the ice cream cart, but there is also a direct path between the ice cream cart and face painting station too • the ice cream cart and ring toss both lead to the fishing game (b) To advertise the event, (i) Can the charity claim each attraction can be visited exactly once? (e.g. does the graph have a Hamilton circuit? or a Hamilton path?) If so, give one example, as proof. (ii) For members of the population that always walk through this park, • can the charity claim that the locals are still able to travel along each walkway exactly once and exit the carnival? (e.g. does the graph have an Euler circuit?) Prove your answer. • can the charity claim that the locals are still able to walk along each walkway within the carnival exactly once? (e.g. does the graph have an Euler path?) Prove your answer.
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