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).

## See also

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."## Referenced on Wolfram|Alpha

Bridged Graph
## Cite this as:

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

## Subject classifications