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, ...