HaskellForMaths-0.4.5: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None

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' :: (Enum t1, Enum a, Num t1, Num a, Ord a, Ord t1) => a -> Graph t1Source

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

l2' :: (Enum t1, Enum a, Num t1, Num a, Ord a, Ord t1) => a -> Graph t1Source

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

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

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 |
Ord DesignVertex |
Show DesignVertex |

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 tSource

schlafli' :: Graph Integer Source

schlafli :: Graph Integer Source

mcLaughlin' :: Graph Integer Source

mcLaughlin :: Graph DesignVertex Source

_McL2 :: [Permutation DesignVertex]Source

_McL :: [Permutation DesignVertex]Source