Theorems · Theorem · combinatorics
SimpleGraph.degree_eq_sum_if_adj
∀ {V : Type u_1} [inst : Fintype V] (G : SimpleGraph V) [inst_1 : DecidableRel G.Adj] {R : Type u_3}
[inst_2 : AddCommMonoidWithOne R] (i : V), ↑(G.degree i) = ∑ j, if G.Adj i j then 1 else 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.ofPredproof · cited by 6,101
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.filterproof · cited by 949
- SimpleGraph.neighborSetstatement · cited by 257
- Set.toFinsetproof · cited by 217
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.lapMatrix_toLinearMap₂'proof · cited by 2