directed cycle

directed cycle

[də¦rek·təd ′sī·kəl]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Second, for any node A, the directed cycle A [right arrow] T [right arrow] S [right arrow] A is of length 3.
The reversal of the orientation of a directed cycle in an [alpha]-orientation yields another [alpha]-orientation.
An NCM is said to be acyclic if it does not possess any directed cycle.
For an integer n [greater than or equal to] 3, the directed cycle of length n is the graph [C.sub.n] whose vertices are 0, 1, ...,n-1 and whose edges are the pairs i, i + 1, where the arithmetic is done modulo n.
Each directed cycle of [D.sub.[phi]] corresponds to a directed cycle of D.
For example, if D is a simple directed cycle, then the intervals yield a division of the cycle into two arcs.
Such a condition was first obtained by Robert (1980), who proved that if G(f) has no directed cycle, then f has a unique fixed point.
A directed cycle is a sequence of directed edges ([i.sub.1], [i.sub.2]), ([i.sub.2], [i.sub.3]), ..., ([i.sub.k-1], [i.sub.1]) such that all [i.sub.1], ..., [i.sub.k] are distinct.
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.