Theorems · Definition · combinatorics
SimpleGraph.degree
{V : Type u_1} → (G : SimpleGraph V) → (v : V) → [Fintype ↑(G.neighborSet v)] → ℕG.degree v is the number of vertices adjacent to v.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 112 results in Mathlib
- Foundations
- Depth 29 from the axioms, rests on 179 definitions · uses propext, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.neighborFinsetproof · cited by 72
Cited by116
Results whose statement or proof uses this declaration.
- SimpleGraph.minDegreeproof · cited by 25
- SimpleGraph.maxDegreeproof · cited by 19
- SimpleGraph.IsRegularOfDegreeproof · cited by 10
- SimpleGraph.card_neighborSet_eq_degreestatement · cited by 9
- SimpleGraph.degMatrixproof · cited by 7
- SimpleGraph.minDegree_le_degreestatement and proof · cited by 6
- SimpleGraph.IsIsolated.degree_eq_zerostatement · cited by 6
- SimpleGraph.card_neighborFinset_eq_degreestatement · cited by 5
- SimpleGraph.card_incidenceFinset_eq_degreestatement · cited by 4
- SimpleGraph.sum_degrees_eq_twice_card_edgesstatement · cited by 4
- SimpleGraph.le_minDegree_of_forall_le_degreestatement and proof · cited by 3
- SimpleGraph.Subgraph.coe_degreestatement · cited by 3