Question: Show that there is a Gray code of order n whenever n is a positive integer, or equivalently, show that the n-cube Qn,n> 1, always has a Hamilton circuit
Fleury's algorithm, published in 1883, constructs Euler circuits by first choosing an arbitrary vertex of a connected multigraph, and then forming a circuit by choosing edges successively. Once an edge is chosen, it is removed. Edges are chosen successively so that each edge begins where the last edge ends, and so that this edge is not a cut edge unless there is no alternative.