Theorems · Inductive type · combinatorics
Matrix.IsAdjMatrix
{α : Type u_1} → {V : Type u_2} → [Zero α] → [One α] → Matrix V V α → PropA : Matrix V V α is qualified as an "adjacency matrix" if
(1) every entry of A is 0 or 1,
(2) A is symmetric,
(3) every diagonal entry of A is 0.
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement · cited by 4,303
Cited by34
Results whose statement or proof uses this declaration.
- Matrix.IsAdjMatrix.toGraphstatement and proof · cited by 9
- Matrix.IsAdjMatrix.zero_or_onestatement and proof · cited by 6
- Matrix.IsAdjMatrix.submatrixstatement and proof · cited by 4
- Matrix.IsAdjMatrix.symmstatement and proof · cited by 3
- Matrix.IsAdjMatrix.toGraph_adjstatement and proof · cited by 3
- Matrix.IsAdjMatrix.apply_diagstatement and proof · cited by 3
- Matrix.IsAdjMatrix.diag_eq_zerostatement and proof · cited by 3
- Matrix.IsAdjMatrix.reindexstatement and proof · cited by 2
- Matrix.IsAdjMatrix.toGraphReindexIsostatement and proof · cited by 2
- Matrix.IsAdjMatrix.toGraphSubmatrixHomstatement and proof · cited by 2
- SimpleGraph.isAdjMatrix_adjMatrixstatement · cited by 2
- Matrix.isAdjMatrix_complstatement · cited by 1