Theorems · Definition · combinatorics
SimpleGraph.edist
{V : Type u_1} → SimpleGraph V → V → V → ℕ∞The extended distance between two vertices is the length of the shortest walk between them.
It is ⊤ if no such walk exists.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Metric
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- iInfproof · cited by 1,690
- SimpleGraph.Walkproof · cited by 915
- SimpleGraph.Walk.lengthproof · cited by 212
Cited by58
Results whose statement or proof uses this declaration.
- SimpleGraph.distproof · cited by 40
- SimpleGraph.eccentproof · cited by 28
- SimpleGraph.ballproof · cited by 9
- SimpleGraph.edist_selfstatement · cited by 6
- SimpleGraph.edist_eq_one_iff_adjstatement and proof · cited by 5
- SimpleGraph.edist_lestatement · cited by 5
- SimpleGraph.eccent_topproof · cited by 4
- SimpleGraph.edist_commstatement and proof · cited by 4
- SimpleGraph.edist_eq_top_of_not_reachablestatement · cited by 4
- SimpleGraph.edist_eq_zero_iffstatement · cited by 4
- SimpleGraph.edist_le_eccentstatement and proof · cited by 4
- SimpleGraph.edist_ne_top_iff_reachablestatement and proof · cited by 4