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IsIsolated ⊥ v
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Mathlib/Combinatorics/SimpleGraph/Basic.lean
@@ -964,6 +964,10 @@ variable {G} in
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theorem Adj.not_isIsolated_right (h : G.Adj u v) : ¬G.IsIsolated v :=
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h.symm.not_isIsolated_left
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+@[simp]
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+theorem isIsolated_bot : IsIsolated ⊥ v := by
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+ simp [← neighborSet_eq_empty]
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+
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theorem eq_bot_iff_isIsolated : G = ⊥ ↔ ∀ v, G.IsIsolated v := by
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simp [eq_bot_iff_forall_not_adj, ← neighborSet_eq_empty, Set.eq_empty_iff_forall_notMem]
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