Relation To Vertex Connectivity
Bridges are closely related to the concept of articulation vertices, vertices that belong to every path between some pair of other vertices. The two endpoints of a bridge are articulation vertices unless they have a degree of 1, although it may also be possible for a non-bridge edge to have two articulation vertices as endpoints. Analogously to bridgeless graphs being 2-edge-connected, graphs without articulation vertices are 2-vertex-connected.
In a cubic graph, every cut vertex is an endpoint of at least one bridge.
Read more about this topic: Bridge (graph Theory)
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