Question: Does every graph with an Eulerian path also have an Eulerian cycle? Does every graph with an Eulerian cycle also have an Eulerian path? Is

Does every graph with an Eulerian path also have an Eulerian cycle? Does every graph with an Eulerian cycle also have an Eulerian path? Is it possible for a graph to have a Hamiltonian cycle but not an Eulerian cycle? Is it possible for a graph to have a Eulerian cycle but not an Hamiltonian cycle
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