A digraph topology on nodes is an unlabeled reflexive transitive digraph, equivalently a preorder.
It corresponds to a finite topology; reflexive loops
may be suppressed in diagrams. The numbers of distinct topologies on
, 2, ... nodes are 1, 3, 9, 33, 139, 718, 4535, ... (OEIS
A001930). Brinkmann and McKay (2005, p. 4)
computed these counts through
.
Digraph Topology
See also
Directed Graph, Transitive DigraphExplore with Wolfram|Alpha
References
Brinkmann, G. and McKay, B. D. "Counting Unlabeled Topologies and Transitive Relations." J. Integer Seq. 8, 05.2.1, 2005. https://cs.uwaterloo.ca/journals/JIS/VOL8/McKay/mckay4.html.Sloane, N. J. A. Sequence A001930/M2817 in "The On-Line Encyclopedia of Integer Sequences."Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.Referenced on Wolfram|Alpha
Digraph TopologyCite this as:
Weisstein, Eric W. "Digraph Topology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DigraphTopology.html