Bridged Graph
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).
See also
Bridgeless Graph, Graph Bridge, k-Edge-Connected GraphExplore with Wolfram|Alpha
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References
Sloane, N. J. A. Sequences A052446 and A263915 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Bridged GraphCite this as:
Weisstein, Eric W. "Bridged Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BridgedGraph.html