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:

Refer to the figure below. a. Find a closed path of length 9 at v5. b. List all the vertices that are not reachable from any other vertex. c. Find circuits of lengths 4, 5, and 6 at v3. d. Which of the circuits found in part (c) are also cycles? VI V5 V2 V3 VA

Eulerize the following graph and identify one Euler circuit in your new graph

Determine the circuit of minimal length in the given graph. NEED STEPS Solution. We can chose any initial vertex, we start from A and we list all the possibilitieswith the corresponding lengths.Path LengthA, B, C, D, A 97A, B, D, C, A 108A, C, B, D, A 141A, C, D, B, A 108A, D, B, C, A 141A, D, C, B, A 97We could also have avoided the circuits in opposite directions.A shortest Hamilton circuit is A, B, C, D, A (or A, D, C, B, A) and it has length 97.