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Draw an undirected graph with 6 vertices that has an Eulerian Cycle and a Hamiltonian Cycle.  The...

  1. Draw an undirected graph with 6 vertices that has an Eulerian Cycle and a Hamiltonian Cycle.  The degree of each vertex must be greater than 2.  List the degrees of the vertices, draw the Hamiltonian Cycle on the graph and give the vertex list of the Eulerian Cycle.

  1. Draw a Bipartite Graph with 10 vertices that has an Eulerian Path and a Hamiltonian Cycle.  The degree of each vertex must be greater than 2.  List the degrees of the vertices, draw the Hamiltonian Cycle on the graph and give the vertex list of the Eulerian Path.

  1. Draw a Complete Graph, Kn, with n > 4 that has a Hamiltonian Cycle but does not have an Eulerian Cycle.  List the degrees of the vertices, draw the Hamiltonian Cycle on the graph and provide justification that there is no Eulerian Cycle.
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