A graph is
Wolfram Language as KEdgeConnectedGraphQ g , k ].
The following table gives the numbers of
OEIS 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, ...
See also Cyclic Edge Connectivity ,
Edge Connectivity ,
Edge Cut ,
Graph Bridge ,
k -Connected GraphExplore with Wolfram|Alpha References Harary, F. Graph Theory. Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Sloane, N. J. A. Sequences A000719 /M1452, A052446 , A052447 , and A052448 in "The On-Line Encyclopedia of Integer Sequences." Referenced on Wolfram|Alpha k-Edge-Connected Graph Cite this as: Weisstein, Eric W. "k-Edge-Connected Graph." From MathWorld https://mathworld.wolfram.com/k-Edge-ConnectedGraph.html
Subject classifications 
-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]. 
-edge-connected graphs for 
-node graphs. 
, 2, ...