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

Safe HaskellNone
LanguageHaskell98

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 a, Ord t, Num a, Num t, Enum a, Enum t) => a -> Graph t Source

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

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

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

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