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Theorems · Theorem · combinatorics

SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj

∀ {R : Type u_1} {α : Type u_2} (G : SimpleGraph α) [inst : MulZeroOneClass R] [inst_1 : DecidableEq α]
  [inst_2 : DecidableRel G.Adj] {a b : α} {e : Sym2 α},
  a ≠ b → ¬G.Adj a b → SimpleGraph.incMatrix R G a e * SimpleGraph.incMatrix R G b e = 0
Defined in
Mathlib.Combinatorics.SimpleGraph.IncMatrix
Cited by
1 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulZeroOneClassDecidableEqDecidableRel
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.incMatrix_mul_transpose · cited by 0SimpleGraph.incMatrix_mul…Set · cited by 53352SetSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSym2 · cited by 737Sym2MulZeroOneClass · cited by 184MulZeroOneClassSet.indicator_of_notMem · cited by 154Set.indicator_of_notMemSet.notMem_empty · cited by 35Set.notMem_emptySimpleGraph.incMatrix · cited by 16SimpleGraph.incMatrixSimpleGraph.incMatrix_apply_mul_incMatrix_apply · cited by 2SimpleGraph.incMatrix_app…SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj · cited by 1SimpleGraph.incidenceSet_…SimpleGraph.incMatrix_apply_m…CITED BYCITES

Cites10

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Cited by1

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