k-Edge-Connected Graph
المؤلف:
Harary, F.
المصدر:
Graph Theory. Reading, MA: Addison-Wesley
الجزء والصفحة:
...
8-3-2022
2170
k-Edge-Connected Graph
A graph is 
-edge-connected if there does not exist a set of 
edges whose removal disconnects the graph (Skiena 1990, p. 177). The maximum edge connectivity of a given graph is the smallest degree of any node, since deleting these edges disconnects the graph. Complete bipartite graphs have maximum edge connectivity.
-edge-connectedness graph checking is implemented in the Wolfram Language as KEdgeConnectedGraphQ[g, k].
The following table gives the numbers of 
-edge-connected graphs for 
-node graphs.
 |
OEIS |
 , 2, ... |
| 0 |
A000719 |
0, 1, 2, 5, 13, 44, 191, ... |
| 1 |
A052446 |
0, 1, 1, 3, 10, 52, 351, ... |
| 2 |
A052447 |
0, 0, 1, 2, 8, 41, 352, ... |
| 3 |
A052448 |
0, 0, 0, 1, 2, 15, 121, ... |
| 4 |
|
0, 0, 0, 0, 1, 3, 25, ... |
| 5 |
|
0, 0, 0, 0, 0, 1, 3, ... |
| 6 |
|
0, 0, 0, 0, 0, 0, 1, ...
|
REFERENCES
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 45, 1994.
Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.
Sloane, N. J. A. Sequences A000719/M1452, A052446, A052447, and A052448 in "The On-Line Encyclopedia of Integer Sequences."
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