Theorems · Theorem · combinatorics

SimpleGraph.incMatrix_mul_transpose

∀ {R : Type u_1} {α : Type u_2} (G : SimpleGraph α) [inst : Fintype (Sym2 α)] [inst_1 : DecidableEq α]
  [inst_2 : DecidableRel G.Adj] [inst_3 : Semiring R] [inst_4 : G.LocallyFinite],
  SimpleGraph.incMatrix R G * (SimpleGraph.incMatrix R G).transpose =
    Matrix.of fun a b => if a = b then ↑(G.degree a) else if G.Adj a b then 1 else 0

Defined in

Mathlib.Combinatorics.SimpleGraph.IncMatrix

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqDecidableRelSemiringSimpleGraph.LocallyFinite