Why it matters

Cut vertices identify single points of failure. Foundational for reliability analysis.

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The architecture

DFS + disc + low.

Root: articulation if 2+ children.

Non-root: articulation if child has low >= disc.

Articulation pointsDFS + lowlinkdisc + lowRoot special casechildren >= 2Non-rootchild low >= parent discAlso finds bridges (edges) with similar low-link logic
Articulation.
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How it works end to end

Compute disc + low in DFS.

Check condition per vertex.

Root child count matters.

Related: bridges use edge condition.