A directed cycle graph is a directed version of a cycle graph, with all the edges being oriented in the same direction.
In a directed graph, a set of edges which contains at least one edge (or arc) from each directed cycle is called a feedback arc set. Similarly, a set of vertices containing at least one vertex from each directed cycle is called a feedback vertex set.
A directed cycle graph has uniform in-degree 1 and uniform out-degree 1.
Directed cycle graphs are Cayley graphs for cyclic groups (see e.g. Trevisan).
Read more about this topic: Cycle Graph
Famous quotes containing the words directed, cycle and/or graph:
“Whether in the field of health, education or welfare, I have put my emphasis on preventive rather than curative programs and tried to influence our elaborate, costly and ill- co-ordinated welfare organizations in that direction. Unfortunately the momentum of social work is still directed toward compensating the victims of our society for its injustices rather than eliminating those injustices.”
—Agnes E. Meyer (18871970)
“The lifelong process of caregiving, is the ultimate link between caregivers of all ages. You and I are not just in a phase we will outgrow. This is lifebirth, death, and everything in between.... The care continuum is the cycle of life turning full circle in each of our lives. And what we learn when we spoon-feed our babies will echo in our ears as we feed our parents. The point is not to be done. The point is to be ready to do again.”
—Paula C. Lowe (20th century)
“In this Journal, my pen is a delicate needle point, tracing out a graph of temperament so as to show its daily fluctuations: grave and gay, up and down, lamentation and revelry, self-love and self-disgust. You get here all my thoughts and opinions, always irresponsible and often contradictory or mutually exclusive, all my moods and vapours, all the varying reactions to environment of this jelly which is I.”
—W.N.P. Barbellion (18891919)