# Expert Answers

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

GraphHhasvertexsetv1,v2,v3,v4,v5andedgesete1,e2,e3 ,e4withedge-endpoint function asfollows:

2. For parts a and b, either draw a graph with the specified properties or explain whyno such graph exists (Note that the graph may have loops or multiple edgesconnecting vertices).

a. Graph with four vertices of degrees 1, 2, 3, and3.

b. Graph with four vertices of degrees 1, 2, 3, and4.

3. Suppose a graph has vertices of degrees 0, 2, 2, 3, and 9. How many edges doesthe graph have? Explain youranswer.

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

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

GraphHhasvertexsetv1,v2,v3,v4,v5andedgesete1,e2,e3 ,e4withedge-endpoint function asfollows:

2. For parts a and b, either draw a graph with the specified properties or explain whyno such graph exists (Note that the graph may have loops or multiple edgesconnecting vertices).

a. Graph with four vertices of degrees 1, 2, 3, and3.

b. Graph with four vertices of degrees 1, 2, 3, and4.

3. Suppose a graph has vertices of degrees 0, 2, 2, 3, and 9. How many edges doesthe graph have? Explain youranswer.

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

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

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