Theorems · Definition · combinatorics
Matrix.IsAdjMatrix.toGraph
{α : Type u_1} →
{V : Type u_2} → {A : Matrix V V α} → [inst : MulZeroOneClass α] → [Nontrivial α] → A.IsAdjMatrix → SimpleGraph VFor A : Matrix V V α and h : IsAdjMatrix A,
h.toGraph is the simple graph whose adjacency matrix is A.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- MulZeroOneClassNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- SimpleGraphstatement · cited by 3,072
- Nontrivialstatement and proof · cited by 2,416
- MulZeroOneClassstatement and proof · cited by 184
- Matrix.IsAdjMatrixstatement and proof · cited by 28
Cited by12
Results whose statement or proof uses this declaration.
- Matrix.IsAdjMatrix.toGraph_adjstatement and proof · cited by 3
- Matrix.IsAdjMatrix.toGraphReindexIsostatement · cited by 2
- Matrix.IsAdjMatrix.toGraphSubmatrixHomstatement · cited by 2
- Matrix.IsAdjMatrix.toGraphReindexIso_applystatement · cited by 0
- Matrix.IsAdjMatrix.toGraphReindexIso_symm_applystatement · cited by 0
- Matrix.IsAdjMatrix.toGraphSubmatrixEmbeddingstatement · cited by 0
- Matrix.IsAdjMatrix.toGraphSubmatrixEmbedding_applystatement · cited by 0
- Matrix.IsAdjMatrix.toGraphSubmatrixHom_applystatement · cited by 0
- Matrix.IsAdjMatrix.toGraph_compl_eqstatement and proof · cited by 0
- SimpleGraph.toGraph_adjMatrix_eqstatement · cited by 0
- Matrix.IsAdjMatrix.adjMatrix_toGraph_eqstatement · cited by 0
- Matrix.IsAdjMatrix.toGraph.congr_simpstatement and proof · cited by 0