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

bridgeless graph | graph bridge | k-edge-connected graph