Equivalently, a graph is circulant if its automorphism group contains a full-length cycle.

Every finite connected vertex-transitive graph contains a Hamiltonian cycle except the five known counterexamples.

This game is also one of the few games for the Family Computer that contains a day/night cycle.

The old Roman calendar of festivals contained a cycle of urban celebrations reaching back to the city's legendary foundation.

The interior contains a cycle of frescoes painted by an unknown artist during the mid-fifteenth century.

It contains a seasonal cycle of mostly traditional songs and instrumental pieces with an emphasis on the natural progression of the year.

Thus every graph on n vertices with more than n 1 edges must contain a cycle.

The cube of every connected graph necessarily contains a Hamiltonian cycle.

This is enough for Victor to check that H does indeed contain a Hamiltonian cycle.

The transition rule is non-injective if and only if this graph contains a cycle in which at least one vertex has two differing state assignments.