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Some graphs stuff (#98)

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Patrick Stevens
2020-02-15 13:41:51 +00:00
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parent 9de323c5e8
commit f41f5226b9
18 changed files with 275 additions and 39 deletions
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Graphs/CycleGraph.agda Normal file
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{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Functions
open import Setoids.Setoids
open import Setoids.Subset
open import Graphs.Definition
open import Sets.FinSet.Definition
open import Sets.FinSet.Lemmas
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Sets.EquivalenceRelations
open import Graphs.PathGraph
module Graphs.CycleGraph where
CycleGraph : (n : ℕ) → .(2 <N n) → Graph _ (reflSetoid (FinSet n))
Graph._<->_ (CycleGraph n _) x y = ((toNat x ≡ succ (toNat y)) || (toNat y ≡ succ (toNat x))) || (((toNat x ≡ 0) && (toNat y ≡ n)) || ((toNat y ≡ 0) && (toNat x ≡ n)))
Graph.noSelfRelation (CycleGraph n _) y (inl (inl x)) = nNotSucc x
Graph.noSelfRelation (CycleGraph n _) y (inl (inr x)) = nNotSucc x
Graph.noSelfRelation (CycleGraph (succ n) _) y (inr (inl (fst ,, snd))) = naughtE (transitivity (equalityCommutative fst) snd)
Graph.noSelfRelation (CycleGraph (succ n) _) y (inr (inr (fst ,, snd))) = naughtE (transitivity (equalityCommutative fst) snd)
Graph.symmetric (CycleGraph n _) (inl (inl x)) = inl (inr x)
Graph.symmetric (CycleGraph n _) (inl (inr x)) = inl (inl x)
Graph.symmetric (CycleGraph n _) (inr (inl x)) = inr (inr x)
Graph.symmetric (CycleGraph n _) (inr (inr x)) = inr (inl x)
Graph.wellDefined (CycleGraph n _) refl refl i = i