5. Determine if the graph contains an Euler circuit. If so, identify an Euler circuit on the graph by number- ing the sequence of edges in the order traveled. If not, explain. Ay the dog &#ibri &

Find a Hamilton circuit for the graph that begins with the specific edge EA and AE 

3) Determine whether the sequence of vertices is a path only, a circuit, or neither in the given graph. Circle the options listed in the part related to the given sequence. A B D E H a) BHFG b) BF G→C ⇒F→B c) GFH →B⇒F⇒C⇒G C PATH ONLY PATH ONLY PATH ONLY CIRCUIT CIRCUIT CIRCUIT NEITHER NEITHER NEITHER

The following graph has 9 vertices. a. Does this graph have an Euler circuit? Why? 22 21 12 b. Does this graph have an Euler path? Why? 20 02 10 01 c. Does this graph have a Hamilton path? Why? 00

1) Definitions. The graph below shows 5 cities. The weights on the edges represent the airfare for a one-way flight between the cities. a. How many vertices and edges does the graph have? b. Is the graph connected? c. What is the degree of the vertex representing LA? d. If you fly from Seattle to Dallas to Atlanta, is that a path or a circuit? And what is its cost? e. If you fly from LA to Chicago to Dallas to LA, is that a path or a circuit? And what is its cost? f. Is the graph a complete graph? If so, how many Hamiltonian circuits does it have? Seattle LA $100 $70 $150- $145 Chicago $170 $75 $120 $140 $165 $85 Atlanta Dallas

13. A mail person decides to park their vehicle and walk through one of the neighborhoods they deliver mail. They want to return to their vehicle without crossing any path twice. Can they get back to their vehicle using the graph K, below? Find the degrees of the vertices, then find an Euler circuit if one exists. h K9 Fill in the degree of each vertex based on the graph. Vertex Degree a b d e f g y Euler circuit:

The graph shown has at least one Euler circuit. Determine an Euler circuit that begins and ends with vertex C. Complete the path so that it is an Euler circuit. C, A, B, E, D, A, 0 ... (.... D B E

6. Determine whether the given graph has an Euler circuit. Construct such a circuit when one exists. If no Euler circuit exists, determine whether the graph has an Euler path and construct such a path if one exists. Write the reason your answer is correct. Euler Circuit: Yes No Euler Path: Yes No b Ø d a Reason: Reason: Euler Path/Circuit: