Theorems · Definition · combinatorics
SimpleGraph.Iso
{V : Type u_1} → {W : Type u_2} → SimpleGraph V → SimpleGraph W → Type (max u_1 u_2)A graph isomorphism is a bijective map on vertex sets that respects adjacency relations.
The notation G ≃g G' represents the type of graph isomorphisms.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjproof · cited by 1,346
- RelIsoproof · cited by 456
Cited by143
Results whose statement or proof uses this declaration.
- SimpleGraph.Iso.symmstatement and proof · cited by 34
- SimpleGraph.Iso.toHomstatement and proof · cited by 13
- SimpleGraph.Iso.reflstatement · cited by 12
- SimpleGraph.Iso.compstatement and proof · cited by 10
- SimpleGraph.Iso.toEmbeddingstatement and proof · cited by 9
- SimpleGraph.copyCountproof · cited by 8
- SimpleGraph.Iso.sumCongrstatement and proof · cited by 7
- SimpleGraph.Iso.toCopystatement and proof · cited by 7
- SimpleGraph.Iso.card_edgeFinset_eqstatement and proof · cited by 6
- SimpleGraph.Iso.mapstatement · cited by 6
- SimpleGraph.completeBipartiteGraphCongrstatement · cited by 5
- SimpleGraph.Iso.connectedComponentEquivstatement and proof · cited by 5