Theorems · Theorem · combinatorics
SimpleGraph.degree_starGraph_of_ne_center
∀ {V : Type u_1} [inst : Fintype V] [inst_1 : DecidableEq V] {r v : V}, v ≠ r → (SimpleGraph.starGraph r).degree v = 1Every non-center vertex of a starGraph has degree one.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Star
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- SimpleGraph.neighborSetstatement · cited by 257
- SimpleGraph.degreestatement · cited by 112
- SimpleGraph.starGraphstatement · cited by 10
- SimpleGraph.degree_eq_one_iff_existsUnique_adjproof · cited by 3
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