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# 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] .

The numbers of simple bridged graphs on , 2, ... vertices are 0, 1, 2, 6, 18, 79, 462, 4344, ... (OEIS A263915).

The numbers of simple connected bridged graphs on , 2, ... vertices are 0, 1, 1, 3, 10, 52, 351, 3714, 63638, 1912203, ... (OEIS A052446).

Bridgeless Graph, Graph Bridge, k-Edge-Connected Graph

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## References

Sloane, N. J. A. Sequences A052446 and A263915 in "The On-Line Encyclopedia of Integer Sequences."

Bridged Graph

## Cite this as:

Weisstein, Eric W. "Bridged Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BridgedGraph.html