Answer the following questions using the network shown to the right.

a$.$ What is the order of the network?

b$.$ What is the degree of each vertex of the network?

c$.$ Does the network have a special form $($such as a tree or a complete network$)?$ If so$,$ what?

d$.$ Does the network have an Euler circuit? Explain.

e$.$ If an Euler circuit does exist, apply the burning bridges rule to find one. Explain the steps of the method and note the vertices at which critical decisions must

be made.

a$.$ The order of the network is

b$.$ What is the degree of each vertex of the network?

Vertices $H$ and $C$ have degree

Vertices E$,$ F$,$ D$,$ A$,$ B$,$ and G have degree

c$.$ Does the network have a special form $($such as a tree or a complete network$)?$ Choose the correct answer below.

A$.$ The network is a tree network.

B$.$ The network is a complete network.

C$.$ The network does not have a special form.

d$.$ Does the network have an Euler circuit?

No

Yes

How do you know that the network has an Euler circuit?

A$.$ Because there are twice as many edges as there are vertices

B$.$ Because each of the vertices have an even degree

C$.$ Because there are an even number of vertices

D$.$ The network has no Euler circuit.

e$.$ If an Euler circuit does exist, apply the burning bridges rule to find one. Explain the steps of the method and note the vertices at which critical decisions must be made.

Type the vertices to complete an Euler circuit, if possible, starting at E$.$ Select the correct choice and, if necessary, fill in any answer box in your choice below.

A$.$ E$,($Use a comma to separate answers as needed.$)$

B$.$ An Euler circuit starting at $E$ is not possible.