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Theorems · Theorem · combinatorics

SimpleGraph.edge_adj

∀ {V : Type u_1} (s t v w : V), (SimpleGraph.edge s t).Adj v w ↔ (v = s ∧ w = t ∨ v = t ∧ w = s) ∧ v ≠ w
Defined in
Mathlib.Combinatorics.SimpleGraph.Operations
Cited by
3 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.edge_self_eq_bot · cited by 3SimpleGraph.edge_self_eq_…SimpleGraph.lt_sup_edge · cited by 1SimpleGraph.lt_sup_edgeSimpleGraph.not_cliqueFree_of_isTuranMaximal · cited by 0SimpleGraph.not_cliqueFre…SimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSym2.mk · cited by 332Sym2.mkSet.mem_singleton_iff · cited by 172Set.mem_singleton_iffSimpleGraph.edge · cited by 44SimpleGraph.edgeSym2.eq_iff · cited by 5Sym2.eq_iffSimpleGraph.fromEdgeSet_adj · cited by 1SimpleGraph.fromEdgeSet_a…SimpleGraph.edge_adjCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.