Theorems · Theorem · combinatorics
SimpleGraph.IsIsolated.degree_eq_zero
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)], G.IsIsolated v → G.degree v = 0Alias of the reverse direction of SimpleGraph.degree_eq_zero.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement · cited by 112
- SimpleGraph.IsIsolatedstatement · cited by 32
- SimpleGraph.degree_eq_zeroproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.minDegree_of_subsingletonproof · cited by 6
- SimpleGraph.maxDegree_of_subsingletonproof · cited by 5
- SimpleGraph.maxDegree_bot_eq_zeroproof · cited by 2
- SimpleGraph.degree_eq_zero_of_subsingletonproof · cited by 1
- SimpleGraph.bot_degreeproof · cited by 1
- SimpleGraph.maxDegree_induce_of_support_subsetproof · cited by 0