Connected Digraph
المؤلف:
Skiena, S
المصدر:
"Strong and Weak Connectivity." §5.1.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley
الجزء والصفحة:
...
9-3-2022
1792
Connected Digraph
There are two distinct notions of connectivity in a directed graph. A directed graph is weakly connected if there is an undirected path between any pair of vertices, and strongly connected if there is a directed path between every pair of vertices (Skiena 1990, p. 173). The following tables summarized the number of weakly and strongly connected digraphs on 
, 2, ... nodes. The 8 weakly but not strongly connected digraphs on three nodes are illustrated above.
| connectivity |
OEIS |
counts |
| weakly connected |
A003085 |
1, 2, 13, 199, 9364, ... |
| strongly connected |
A035512 |
1, 1, 5, 83, 5048, 1047008, ... |
| weakly but not strongly |
A056988 |
0, 1, 8, 116, 4316, 483835, ...
|
REFERENCES
Skiena, S. "Strong and Weak Connectivity." §5.1.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 172-174, 1990.
Sloane, N. J. A. Sequences A003085/M2067, A035512, and A056988 in "The On-Line Encyclopedia of Integer Sequences."
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