The name "bridged graph" is used here for a graph that contains one or more graph bridges. Examples of bridged graphs include nontrivial path graphs, positive-order ladder rung graphs, the bull graph, nontrivial star graphs, and trees on at least two vertices.
A graph that is not bridged is said to be bridgeless. A connected graph on at least two vertices
can be tested for being bridged in the Wolfram
Language using Not[KEdgeConnectedGraphQ[g,
2]] or EdgeConnectivity[g]
.
The numbers of unlabeled simple bridged graphs on 
,
2, ... vertices are 0, 1, 2, 6, 18, 79, 462, 4344,
... (OEIS A263915).
The numbers of unlabeled simple connected bridged graphs on 
, 2, ... vertices are 0,
1, 1, 3, 10, 52, 351, 3714, 63638, 1912203, ... (OEIS A052446).
