Theorems · Theorem · combinatorics
SimpleGraph.radius_ne_top_iff
∀ {α : Type u_1} {G : SimpleGraph α} [Nonempty α] [Finite α], G.radius ≠ ⊤ ↔ G.Connected- Defined in
- Mathlib.Combinatorics.SimpleGraph.Diam
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- Finitestatement and proof · cited by 3,029
- SimpleGraph.Connectedstatement and proof · cited by 75
- SimpleGraph.edistproof · cited by 55
- SimpleGraph.Connected.preconnectedproof · cited by 28
- Not.imp_symmproof · cited by 25
- SimpleGraph.radiusstatement and proof · cited by 20
- SimpleGraph.edist_ne_top_iff_reachableproof · cited by 4
- SimpleGraph.radius_eq_top_of_not_connectedproof · cited by 2
- SimpleGraph.exists_edist_eq_radius_of_finiteproof · cited by 1
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