# directed cycle

## directed cycle

[də¦rek·təd ′sī·kəl]
(mathematics)
References in periodicals archive ?
The reversal of the orientation of a directed cycle in an [alpha]-orientation yields another [alpha]-orientation.
Since the orientation, clockwise or counterclockwise, of a directed cycle in G' and G# is identical the distributive lattices of [alpha]'-orientations are isomorphic.
An NCM is said to be acyclic if it does not possess any directed cycle.
For example, if D is a simple directed cycle, then the intervals yield a division of the cycle into two arcs.
If D is a simple directed cycle, then respecting intervals means preserving the orientation of the cycle.
n] a local interaction graph G f(x), which is a subgraph of G(f) defined as the directed graph whose the adjacency matrix is the discrete Jacobian matrix of f evaluated at point x, and they proved that if G f(x) hasno directed cycle for all x in [{0,1}.
Finally, in Section 6, we compare F with the well-known class F' of networks f whose the interaction graph G(f) is a directed cycle.
Matrix of membership (cycles matrix) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] relating the arcs and graph directed cycles of a network, indicating membership pipes to network ring and having on the lines, order number of rings M, and the columns at the arcs T.
In particular, if D is an orientation of G that contains no odd directed cycles, then it has the required property (Theorem 34).
The De Bruijn graph has been much studied, especially in connection with combinatorics on words, and one of its well known properties is the fact that its number of directed cycles of length d, for d [less than or equal to] n, is given by

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