1. Given the following graph, answer the questions below: 0 0 a) Hamiltonian Cycles and Paths: i. Is it possible to determine if the graph has a Hamiltonian Cycle by using Dirac's Theorem? Justify your answer. What can you conclude about the existence of a Hamiltonian Cycle? ii. Is the graph Bipartite? Justify your answer. If the graph is Bipartite, is it Complete? Justify your answer. What can you conclude about the existence of a Hamiltonian Cycle? Hamiltonian Path? Justify your answer. iii. Is it possible to find a Hamiltonian Cycle in the graph using trial-and-crror? If so, draw it on a copy of the graph and give the vertex list for H.C. Otherwise justify your answer then determine if it's possible to find a Hamiltoi Ph. If so, draw it on a copy of the graph and give the vertex list for the H.P, otherwise justify your