Theorems · Theorem · combinatorics

SimpleGraph.adjMatrix_mulVec_apply

∀ {α : Type u_1} {V : Type u_2} (G : SimpleGraph V) [inst : DecidableRel G.Adj] [inst_1 : Fintype V]
  [inst_2 : NonAssocSemiring α] (v : V) (vec : V → α),
  (SimpleGraph.adjMatrix α G).mulVec vec v = ∑ u ∈ G.neighborFinset v, vec u

Defined in

Mathlib.Combinatorics.SimpleGraph.AdjMatrix

Cited by

4 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableRelFintypeNonAssocSemiring