Theorems · Theorem · combinatorics

SimpleGraph.natCast_card_dart_eq_dotProduct

∀ {α : Type u_1} {V : Type u_2} (G : SimpleGraph V) [inst : DecidableRel G.Adj] [inst_1 : Fintype V]
  [inst_2 : NonAssocSemiring α], ↑(Fintype.card G.Dart) = (SimpleGraph.adjMatrix α G).mulVec 1 ⬝ᵥ 1

The number of all darts in a simple finite graph is equal to the dot product of G.adjMatrix α *ᵥ 1 and 1.

Defined in

Mathlib.Combinatorics.SimpleGraph.AdjMatrix

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableRelFintypeNonAssocSemiring