Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.Iso.connectedComponentEquiv

{V : Type u} →
  {V' : Type v} → {G : SimpleGraph V} → {G' : SimpleGraph V'} → G ≃g G' → G.ConnectedComponent ≃ G'.ConnectedComponent

An isomorphism of graphs induces a bijection of connected components.

Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
Cited by
5 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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SimpleGraph.Iso.connectedComponentEquiv_apply · cited by 0Iso.connectedComponentEqu…SimpleGraph.Iso.connectedComponentEquiv_refl · cited by 0Iso.connectedComponentEqu…SimpleGraph.Iso.connectedComponentEquiv_symm · cited by 0Iso.connectedComponentEqu…SimpleGraph.Iso.connectedComponentEquiv_symm_apply · cited by 0Iso.connectedComponentEqu…SimpleGraph.Iso.connectedComponentEquiv_trans · cited by 0Iso.connectedComponentEqu…SimpleGraph.ConnectedComponent.isoEquivSupp · cited by 0ConnectedComponent.isoEqu…Equiv · cited by 8337EquivSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Iso · cited by 99SimpleGraph.IsoSimpleGraph.ConnectedComponent · cited by 86SimpleGraph.ConnectedComp…RelIso.toRelEmbedding · cited by 34RelIso.toRelEmbeddingSimpleGraph.Iso.symm · cited by 34Iso.symmRelEmbedding.toRelHom · cited by 15RelEmbedding.toRelHomSimpleGraph.ConnectedComponent.map · cited by 11ConnectedComponent.mapIso.connectedComponentEquivCITED BYCITES

Cites8

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Cited by6

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