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

Safe Haskell | None

Math.Combinatorics.GraphAuts

Synopsis

- isVertexTransitive :: Ord t => Graph t -> Bool
- isEdgeTransitive :: Ord t => Graph t -> Bool
- isArcTransitive :: Ord t => Graph t -> Bool
- is2ArcTransitive :: Ord t => Graph t -> Bool
- is3ArcTransitive :: Ord t => Graph t -> Bool
- isnArcTransitive :: Ord t => Int -> Graph t -> Bool
- isDistanceTransitive :: Ord t => Graph t -> Bool
- graphAuts :: Ord a => Graph a -> [Permutation a]
- incidenceAuts :: (Ord p, Ord b) => Graph (Either p b) -> [Permutation p]
- graphIsos :: (Ord t1, Ord t) => Graph t -> Graph t1 -> [[(t, t1)]]
- incidenceIsos :: (Ord t3, Ord t1, Ord t2, Ord t) => Graph (Either t2 t) -> Graph (Either t3 t1) -> [[(t2, t3)]]
- isGraphIso :: (Ord a, Ord b) => Graph a -> Graph b -> Bool
- isIncidenceIso :: (Ord p1, Ord b1, Ord p2, Ord b2) => Graph (Either p1 b1) -> Graph (Either p2 b2) -> Bool

# Documentation

isVertexTransitive :: Ord t => Graph t -> Bool Source

A graph is vertex-transitive if its automorphism group acts transitively on the vertices. Thus, given any two distinct vertices, there is an automorphism mapping one to the other.

isEdgeTransitive :: Ord t => Graph t -> Bool Source

A graph is edge-transitive if its automorphism group acts transitively on the edges. Thus, given any two distinct edges, there is an automorphism mapping one to the other.

isArcTransitive :: Ord t => Graph t -> Bool Source

A graph is arc-transitive (or flag-transitive) if its automorphism group acts transitively on arcs. (An arc is an ordered pair of adjacent vertices.)

is2ArcTransitive :: Ord t => Graph t -> Bool Source

is3ArcTransitive :: Ord t => Graph t -> Bool Source

isnArcTransitive :: Ord t => Int -> Graph t -> Bool Source

A graph is n-arc-transitive is its automorphism group is transitive on n-arcs. (An n-arc is an ordered sequence (v0,...,vn) of adjacent vertices, with crossings allowed but not doubling back.)

isDistanceTransitive :: Ord t => Graph t -> Bool Source

A graph is distance transitive if given any two ordered pairs of vertices (u,u') and (v,v') with d(u,u') == d(v,v'), there is an automorphism of the graph that takes (u,u') to (v,v')

graphAuts :: Ord a => Graph a -> [Permutation a]Source

Given a graph g, `graphAuts g` returns generators for the automorphism group of g. If g is connected, then the generators will be a strong generating set.

incidenceAuts :: (Ord p, Ord b) => Graph (Either p b) -> [Permutation p]Source

Given the incidence graph of an incidence structure between points and blocks (for example, a set system), `incidenceAuts g` returns generators for the automorphism group of the incidence structure. The generators are represented as permutations of the points. The incidence graph should be represented with the points on the left and the blocks on the right. If the incidence graph is connected, then the generators will be a strong generating set.

graphIsos :: (Ord t1, Ord t) => Graph t -> Graph t1 -> [[(t, t1)]]Source

incidenceIsos :: (Ord t3, Ord t1, Ord t2, Ord t) => Graph (Either t2 t) -> Graph (Either t3 t1) -> [[(t2, t3)]]Source

isGraphIso :: (Ord a, Ord b) => Graph a -> Graph b -> Bool Source

Are the two graphs isomorphic?

isIncidenceIso :: (Ord p1, Ord b1, Ord p2, Ord b2) => Graph (Either p1 b1) -> Graph (Either p2 b2) -> Bool Source

Are the two incidence structures represented by these incidence graphs isomorphic?