 TOPICS  # Bridgeless Graph

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).

Bridged Graph, Cycle Double Cover Conjecture, Graph Bridge, k-Edge-Connected Graph

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## References

Sloane, N. J. A. Sequences A007146/M2909 and A263914 in "The On-Line Encyclopedia of Integer Sequences."

Bridgeless Graph

## Cite this as:

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