HaskellForMaths-0.4.9: 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 a => Graph a -> Maybe (Int, Int, Int, Int) Source #

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

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

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

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

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

paleyGraph :: (Ord t, Num 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

Instances details

Eq DesignVertex Source # |
Instance details Defined in Math.Combinatorics.StronglyRegularGraph Methods (==) :: DesignVertex -> DesignVertex -> Bool (/=) :: DesignVertex -> DesignVertex -> Bool
Ord DesignVertex Source # |

Instance details

Defined in Math.Combinatorics.StronglyRegularGraph

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 # |
Instance details Defined in Math.Combinatorics.StronglyRegularGraph 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 #