Investigations on graph-theoretical constructions in Homotopy type theory

{-# OPTIONS --without-K --exact-split #-}
open import foundations.Core using (Level)
module lib.graph-families.CompleteGraph (ℓ : Level)
  where
  open import foundations.Core
  open import lib.graph-definitions.Graph
  open Graph
  open import foundations.Fin ℓ

Complete graph \(K_n\)

A graph of \(n : \N\) vertices is called when every pair of nodes is joint by an edge. When the nodes are of type \(\Fin{n}\), the complete graph is denoted by denoted by \(K_{n}\).

  Complete :  (n : ℕ) → Graph ℓ
  Complete n
    = graph (Fin n)
            (λ _ _ → 𝟙 ℓ)
            (Fin-is-set)
            (λ _ _ → 𝟙-is-set)
  syntax Complete n = 𝕂 n

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