Theorems · Theorem · combinatorics
SimpleGraph.ediam_eq_top_of_not_connected
∀ {α : Type u_1} {G : SimpleGraph α} [Nonempty α], ¬G.Connected → G.ediam = ⊤- Defined in
- Mathlib.Combinatorics.SimpleGraph.Diam
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- eq_top_iffproof · cited by 236
- SimpleGraph.Reachableproof · cited by 141
- SimpleGraph.Connectedstatement and proof · cited by 75
- SimpleGraph.ediamstatement and proof · cited by 44
- SimpleGraph.connected_iff_exists_forall_reachableproof · cited by 6
- SimpleGraph.edist_eq_top_of_not_reachableproof · cited by 4
- SimpleGraph.edist_le_ediamproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.ediam_botproof · cited by 1
- SimpleGraph.ediam_eq_top_of_not_preconnectedproof · cited by 1
- SimpleGraph.diam_eq_zero_of_not_connectedproof · cited by 0