4. Given the graph below; a. Determine if the graph has an Eulerian Cycle without using...

 

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4. Given the graph below; a. Determine if the graph has an Eulerian Cycle without using trial-and-error to find it. Thoroughly justify your answer. b. Determine if the graph has an Eulerian Path without using trial-and-error to find it. Thoroughly justify your answer. c. Find a Hamiltonian Cycle starting at vertex A. Draw the Hamiltonian Cycle on the graph and list the vertices of the cycle. H M Note: A Hamiltonian Cycle is a simple cycle that traverses all vertices. A simple cycle starts at a vertex, visits other vertices once then returns to the starting vertex. For instance if the vertices of Ks were labeled A, B, C, D, E, one Hamiltonian Cycle would be ABCDEA. 4. Given the graph below; a. Determine if the graph has an Eulerian Cycle without using trial-and-error to find it. Thoroughly justify your answer. b. Determine if the graph has an Eulerian Path without using trial-and-error to find it. Thoroughly justify your answer. c. Find a Hamiltonian Cycle starting at vertex A. Draw the Hamiltonian Cycle on the graph and list the vertices of the cycle. H M Note: A Hamiltonian Cycle is a simple cycle that traverses all vertices. A simple cycle starts at a vertex, visits other vertices once then returns to the starting vertex. For instance if the vertices of Ks were labeled A, B, C, D, E, one Hamiltonian Cycle would be ABCDEA.