Euler Paths and Circuits Quiz

Using the following graph, find an Euler path that starts with vertex A.

• No Euler path exists.

• A → C → D → A → B → D

• A → B → D → C

• B → A → D → C

Using the following graph, find an Euler path that starts with vertex B.

• B → E → D → A → C → E → D

• B → A → D → E → C

• No Euler path exists.

• B → A → D → E → B → C → A → E → C → D

Using the following graph, find an Euler circuit that begins and ends with vertex A.

• A → B → C → D → B → E → A

• No Euler circuit exists.

• A → B → C → D → B → A

• A → B → C → D → E → A → B

Using the following graph, find an Euler circuit that begins and ends with vertex B.

• B → C → D → E → F → A → B → D → F → B

• B → C → D → E → F → A → B → C → D → B → F → D → B

• B → A → F → E → D → C → B

• No Euler circuit exists.

Using the following graph, find an Euler circuit that begins and ends with vertex A.

• No Euler circuit exists.

• A → B → D → E → C → A

• A → B → D → C → E → D → A

• A → D → B → A → C → E → D → C → A

The map shows the states Tennessee, Alabama, Georgia, and Mississippi. Is it possible to find a route that starts in Tennessee and crosses each common state border exactly one time?

• No

• Yes

For the floor plan below, is it possible to find a path that starts in room C and passes through each doorway exactly one time?

• No

• Yes

For the following floor plan, is it possible to find a route that begins in one room, passes through each doorway exactly once, and ends in the starting room?

• No

• Yes

The map shows the states New Mexico, Oklahoma, Texas, Arkansas, and Louisiana. Find a route that starts in Arkansas and crosses each common state border exactly one time.

• AR → TX → NM → OK → TX → LA

• AR → OK → NM → TX → AR → LA → TX → OK

• No such route exists.

• AR → LA → TX → NM → OK → AR

Using the following floor plan, find a path that begins and ends in room F and passes through each doorway exactly once.

• F → E → G → B → C → D → G → A

• F → A → G → D → C → B → G → A → F

• F → A → G → B → C → D → G → E → F

• No such route exists.