HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Combinatorics.StronglyRegularGraph

Description

A module defining various strongly regular graphs, including the Clebsch, Hoffman-Singleton, Higman-Sims, and McLaughlin graphs.

A strongly regular graph with parameters (n,k,lambda,mu) is a (simple) graph with n vertices, in which the number of common neighbours of x and y is k, lambda or mu according as whether x and y are equal, adjacent, or non-adjacent. (In particular, it is a k-regular graph.)

Strongly regular graphs are highly symmetric, and have large automorphism groups.

# Documentation

srgParams :: Ord t => Graph t -> Maybe (Int, Int, Int, Int) Source #

isSRG :: Ord t => Graph t -> Bool Source #

t' :: (Num a, Num t, Enum a, Enum t, Ord t, Ord a) => a -> Graph t Source #

t :: (Enum a, Num a, Ord a) => a -> Graph [a] Source #

l2' :: (Num a, Num t, Enum a, Enum t, Ord t, Ord a) => a -> Graph t Source #

l2 :: (Enum a, Num a, Ord a) => a -> Graph (a, a) Source #

paleyGraph :: (Num t, Ord t) => [t] -> Graph t Source #

clebsch' :: Graph Integer Source #

clebsch :: Graph [Integer] Source #

clebsch2 :: Graph DesignVertex Source #

triples :: [[Integer]] Source #

heptads :: [[[Integer]]] Source #

(+^) :: Ord a => [[a]] -> Permutation a -> [[a]] Source #

(+^^) :: Ord a => [[a]] -> [Permutation a] -> [[[a]]] Source #

hoffmanSingleton' :: Graph Integer Source #

hoffmanSingleton :: Graph (Either [[Integer]] [Integer]) Source #

inducedA7 :: Permutation Integer -> Permutation (Either [[Integer]] [Integer]) Source #

hsA7 :: [Permutation Integer] Source #

gewirtz' :: Graph Integer Source #

gewirtz :: Graph [Integer] Source #

data DesignVertex Source #

Constructors

C |
P Integer |
B [Integer] |

Instances

Eq DesignVertex Source # |
Methods (==) :: DesignVertex -> DesignVertex -> Bool # (/=) :: DesignVertex -> DesignVertex -> Bool #
Ord DesignVertex Source # |
Methods compare :: DesignVertex -> DesignVertex -> Ordering # (<) :: DesignVertex -> DesignVertex -> Bool # (<=) :: DesignVertex -> DesignVertex -> Bool # (>) :: DesignVertex -> DesignVertex -> Bool # (>=) :: DesignVertex -> DesignVertex -> Bool # max :: DesignVertex -> DesignVertex -> DesignVertex # min :: DesignVertex -> DesignVertex -> DesignVertex #
Show DesignVertex Source # |
Methods showsPrec :: Int -> DesignVertex -> ShowS # show :: DesignVertex -> String # showList :: [DesignVertex] -> ShowS #

higmanSimsGraph' :: Graph Integer Source #

higmanSimsGraph :: Graph DesignVertex Source #

inducedM22 :: Permutation Integer -> Permutation DesignVertex Source #

higmanSimsM22 :: [Permutation Integer] Source #

_HS2 :: [Permutation DesignVertex] Source #

_HS :: [Permutation DesignVertex] Source #

sp2 :: Int -> Graph [F2] Source #

sp :: Int -> Graph [F2] Source #

switch :: Ord t => Graph t -> [t] -> Graph t Source #

schlafli' :: Graph Integer Source #

schlafli :: Graph Integer Source #

mcLaughlin' :: Graph Integer Source #

mcLaughlin :: Graph DesignVertex Source #

_McL2 :: [Permutation DesignVertex] Source #

_McL :: [Permutation DesignVertex] Source #