A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include
complete graphs on nodes, cycle graphs, the
diamond graph, empty
graphs, and the singleton graph.

Connected bridgeless graphs are 2-edge connected and can be tested for in the Wolfram Language using `KEdgeConnectedGraphQ`[*g*,
2] or `EdgeConnectivity`[*g*]
.

A graph that is not bridgeless is said to be bridged.

The numbers of simple bridgeless graphs on , 2, ... vertices are 1, 1, 2, 5, 16, 77, 582, 8002, ...
(OEIS A263914).

The numbers of simple connected bridgeless graphs on , 2, ... vertices are 1, 0, 1, 3, 11, 60, 502, 7403 ... (OEIS
A007146).

## See also

Bridged Graph,

Cycle Double Cover Conjecture,

Graph Bridge,

*k*-Edge-Connected
Graph
## Explore with Wolfram|Alpha

## References

Sloane, N. J. A. Sequences A007146/M2909 and A263914 in "The On-Line Encyclopedia
of Integer Sequences."## Referenced on Wolfram|Alpha

Bridgeless Graph
## Cite this as:

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

## Subject classifications