Theorems · Definition · combinatorics

SimpleGraph.Iso.mapNeighborSet

{V : Type u_1} →
  {W : Type u_2} →
    {G : SimpleGraph V} → {G' : SimpleGraph W} → (f : G ≃g G') → (v : V) → ↑(G.neighborSet v) ≃ ↑(G'.neighborSet (f v))

A graph isomorphism induces an equivalence of neighbor sets.

Defined in: Mathlib.Combinatorics.SimpleGraph.Maps
Cited by: 3 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Quot.sound

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Equivstatement · cited by 8,337
Set.Elemstatement and proof · cited by 7,166
SimpleGraphstatement and proof · cited by 3,072
SimpleGraph.Adjstatement · cited by 1,346
SimpleGraph.neighborSetstatement and proof · cited by 257
SimpleGraph.Isostatement and proof · cited by 99
SimpleGraph.Iso.symmproof · cited by 34

Cited by3

Results whose statement or proof uses this declaration.

SimpleGraph.Iso.degree_eqproof · cited by 2
SimpleGraph.Iso.mapNeighborSet_apply_coestatement and proof · cited by 0
SimpleGraph.Iso.mapNeighborSet_symm_apply_coestatement and proof · cited by 0