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.