# Expert Answers

1. Draw the picture of the specified graph (including any isolated vertices):

with edge-endpoint function as follows:}e1, e2 , e3 , e4 {and edge set }v1, v2 , v3 , v4 , v5 {Graph H has vertex set

2. For parts a and b, either draw a graph with the specified properties or explain why no such graph exists (Note that the graph may have loops or multiple edges connecting vertices).

a. Graph with four vertices of degrees 1, 2, 3, and 3.

b. Graph with four vertices of degrees 1, 2, 3, and 4.

3. Suppose a graph has vertices of degrees 0, 2, 2, 3, and 9. How many edges does the graph have? Explain your answer.

4. Consider the following graph and determine the degree of each vertex of this graph.

5. For each graph, determine whether an Euler circuit exists. If the graph does not have an Euler circuit, explain why. If it does have an Euler circuit, describe one by listing all vertices in the circuit.

with edge-endpoint function as follows:}e1, e2 , e3 , e4 {and edge set }v1, v2 , v3 , v4 , v5 {Graph H has vertex set

2. For parts a and b, either draw a graph with the specified properties or explain why no such graph exists (Note that the graph may have loops or multiple edges connecting vertices).

a. Graph with four vertices of degrees 1, 2, 3, and 3.

b. Graph with four vertices of degrees 1, 2, 3, and 4.

3. Suppose a graph has vertices of degrees 0, 2, 2, 3, and 9. How many edges does the graph have? Explain your answer.

4. Consider the following graph and determine the degree of each vertex of this graph.

5. For each graph, determine whether an Euler circuit exists. If the graph does not have an Euler circuit, explain why. If it does have an Euler circuit, describe one by listing all vertices in the circuit.

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