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If I have four vertices, each of which are adjacent to two others, how are the Hamiltonian circuits for those vertices typically counted? If I envision the unit circle of the real plane’s axis intersection points as the vertices in question, the unit circle indicates at least one path; is it ever convention in such a case to indicate more than one path, i.e. depending on starting point, direction, etc.?

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    $\begingroup$ It is conventional to count just one Hamiltonian cycle independent of its starting point. $\endgroup$ – David G. Stork Apr 20 at 20:44

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