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Question 11 pts

Consider the following graph.

$C:\Users\AD\Desktop\1..JPG$

What’s the degree of vertex B?

	1
	4

	3
	2

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Question 21 pts

Consider the following graph.

$C:\Users\AD\Desktop\2..JPG$

What’s the degree of vertex H?

	3
	1

	4
	2

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Question 31 pts

Consider the following graph.

$C:\Users\AD\Desktop\3.JPG$

Does this graph have an Euler circuit?

	Yes
	Impossible to tell

	Maybe
	No

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Question 41 pts

Consider a "disconnected" graph with six vertices such that each vertex has degree 2. Would such a graph have an Euler circuit or Euler path?

	No
	Yes

	May or may not have an Euler circuit
	Does not have an Euler circuit, but does have an Euler path

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Question 52 pts

Consider the following graph.

$C:\Users\AD\Desktop\5.JPG$

Which of the following statement is true?

	The graph has an Euler path but not an Euler circuit
	The graph has both an Euler circuit and an Euler path

	The graph has an Euler circuit, but not an Euler path
	The graph has neither an Euler circuit nor an Euler path

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Question 62 pts

Consider the following graph.

$C:\Users\AD\Desktop\6.JPG$

Which of the following statement is true?

	The graph has both an Euler circuit and an Euler path
	The graph has an Euler circuit, but not an Euler path

	The graph has an Euler path, but not an Euler circuit
	The graph has neither an Euler circuit nor an Euler path

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Question 72 pts

Consider the following graph.

$C:\Users\AD\Desktop\7.JPG$

Which of the following statement is true?

	The graph has neither an Euler circuit nor an Euler path
	The graph has both an Euler circuit and an Euler path

	The graph has an Euler circuit, but not an Euler path
	The graph has an Euler path, but not an Euler circuit

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Question 82 pts

Consider the following graph.

$C:\Users\AD\Desktop\8.JPG$

Which of the following statement is true?

	The graph has both an Euler circuit and an Euler path
	The graph has an Euler path, but not an Euler circuit

	The graph has an Euler circuit, but not an Euler path
	The graph has neither an Euler circuit nor an Euler path

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Question 92 pts

Consider the following graph.

$C:\Users\AD\Desktop\9.JPG$

Which of the following statement is true?

	The graph has an Euler circuit
	The graph has both an Euler circuit and an Euler path

	The graph has an Euler path
	The graph has neither an Euler circuit nor an Euler path

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Question 102 pts

Consider the following graph. Ignore the weights written on edges.

$C:\Users\AD\Desktop\10..JPG$

Which of the following statement is true?

	The graph has neither an Euler circuit nor an Euler path
	The graph has both an Euler circuit and an Euler path

	The graph has an Euler path
	The graph has an Euler circuit

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Question 114 pts

This exercise comes to you courtesy of Euler himself. Here is the question in Euler’s own words, accompanied by the diagram shown below.

$C:\Users\AD\Desktop\11.JPG$ Let us take an example of two islands with four rivers forming the surrounding water. There are fifteen bridges marked a, b, c, d, etc., across the water around the islands and the adjoining rivers. The question is whether a journey can be arranged that will pass over all the bridges but not over any of them more than once.

What is the answer to Euler’s question? Would the “journey” be possible? Choose one from the following. Hint: Here is a better diagram of the figure.

$C:\Users\AD\Desktop\hw8-4.JPG$

	The graph has both an Euler circuit and an Euler path
	The graph has an Euler path

	The graph has neither an Euler circuit nor an Euler path
	The graph has an Euler circuit