bot_strongly_regular — Mathlib

English

The bound on offDiag for equipartitions in a refined form with a 0 ≤ ε ≤ bound.

Русский

Граница на offDiag для разбиения на более точном виде с 0 ≤ ε ≤ граница.

LaTeX

$$P.IsEquipartition → (0 ≤ ε) → (#(P.parts.biUnion offDiag)).card.cast ≤ (#A * (#A + #P.parts)) / #P.parts$$

Lean4

/-- Empty graphs are strongly regular. Note that `ℓ` can take any value
for empty graphs, since there are no pairs of adjacent vertices. -/
theorem bot_strongly_regular : (⊥ : SimpleGraph V).IsSRGWith (Fintype.card V) 0 ℓ 0
    where
  card := rfl
  regular := bot_degree
  of_adj _ _ h := h.elim
  of_not_adj v w
    _ := by
    simp only [card_eq_zero, Fintype.card_ofFinset, forall_true_left, not_false_iff, bot_adj]
    ext
    simp [mem_commonNeighbors]

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