Theorems · Theorem · combinatorics
SimpleGraph.diam_eq_zero_iff_ediam_eq_top
∀ {α : Type u_1} {G : SimpleGraph α} [Nontrivial α], G.diam = 0 ↔ G.ediam = ⊤- Defined in
- Mathlib.Combinatorics.SimpleGraph.Diam
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- Nontrivialstatement and proof · cited by 2,416
- not_iff_notproof · cited by 159
- SimpleGraph.ediamstatement · cited by 44
- SimpleGraph.diamstatement · cited by 15
- SimpleGraph.ediam_ne_top_of_diam_ne_zeroproof · cited by 2
- SimpleGraph.diam_ne_zero_of_ediam_ne_topproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.connected_iff_diam_ne_zeroproof · cited by 0