Theorems · Theorem · combinatorics
SimpleGraph.edist_eq_one_iff_adj
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V}, G.edist u v = 1 ↔ G.Adj u vThe extended distance between vertices is equal to 1 if and only if these vertices are adjacent.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Metric
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- le_antisymmproof · cited by 2,068
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.Walkproof · cited by 915
- SimpleGraph.Walk.lengthproof · cited by 212
- SimpleGraph.ediststatement and proof · cited by 55
- SimpleGraph.Adj.neproof · cited by 39
- Order.one_le_iff_posproof · cited by 27
- SimpleGraph.Adj.toWalkproof · cited by 22
- Nat.cast_eq_oneproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.eccent_le_one_iffproof · cited by 1
- SimpleGraph.two_lt_edist_iffproof · cited by 1
- SimpleGraph.edist_le_one_iff_adj_or_eqproof · cited by 1
- SimpleGraph.dist_eq_one_iff_adjproof · cited by 1
- SimpleGraph.eq_top_iff_forall_eccent_eq_oneproof · cited by 1