Labelled: BoolElt Default: true
Directed: BoolElt Default: true
Given a finite group A defined on generating set X, construct the
Cayley graph C of A relative to the generating set X. This graph
is defined as follows: The vertices correspond to the elements of A
and two vertices u, v are adjacent if and only if there exists an
element x in X such that u * x = v.
The optional parameter Labelled (Labelled := true by default)
can be set to false to prevent the graph being labelled. If this is not
done, then the vertices of C will be labelled with the appropriate
elements of A and the (directed) edge from u to v will be labelled
with the appropriate element x as defined above.
The parameter Directed (Directed := true by default) may be
used to return the Cayley graph of G as an undirected graph
Labelled: BoolElt Default: true
Directed: BoolElt Default: true
Given a finite group A defined on the generating set X and a
subgroup B of A, construct the Schreier coset graph S for A
over B, relative to X. The graph S is defined as follows:
The vertices correspond to the cosets of B in A, and two vertices
u, v are adjacent in S if and only if there exists an element x
in X such that u * x = v.
The graph is available in both a labelled and an unlabelled version and
directed and undirected versions. These versions are controlled by the
parameters Labelled and Directed, which are both true by
default.
Let P be a transitive permutation group acting on the set
Ω = {1, ..., n}. Let u be an element of Ω and let
T = {t1, ..., tr} be a subset of Ω. This function
constructs the underlying graph G of the digraph corresponding
to the union of P-orbits containing the pairs
(u, t1), ..., (u, tr). Thus, if T defines a self-paired
orbit Δ of the stabilizer in P of the point u, this
function constructs the orbital graph associated with Δ.
Let P be a permutation group acting on the set
Ω = {1, ..., n}. Let G be a graph (digraph) with vertices
v1, ..., vn. This function adds the minimum number of edges to
G so as to produce a graph (digraph) H which is left invariant by
the group P.
The Paley graph of GF(q) where q must be a prime power equivalent to 1
mod 4. Vertices are in bijection with elements of GF(q) and distinct
elements are adjacent when their difference is a square in the field.
The Paley tournament of GF(q) where q must be a prime power equivalent to 3
mod 4. Vertices are in bijection with elements of GF(q) and there is an
edge from u to v when u ≠v and v - u is a square in the field.
Given an incidence structure D = (X, B),
construct the incidence graph G of D.
The vertices of G is X ∪B. The adjacency rules are as follows:
No two vertices of X are adjacent; no two vertices of B are
adjacent; a vertex x ∈X is adjacent to a vertex b ∈B
if and only if x is in b.
Given an incidence structure D = (X, B),
construct the point graph G of D. The
vertex-set of G is X. Vertices x ∈X, y ∈X are adjacent
in G if there is a block b∈B such that x ∈b and y ∈b.
The block graph of the incidence structure D; i.e. the point graph of the dual of D.
Given a plane P with point-set V and line-set L, construct the
incidence graph G of P.
The vertex-set of G is V ∪L. The adjacency rules are as follows:
No two vertices of V are adjacent; no two vertices of L are
adjacent; a vertex v ∈V is adjacent to a vertex a ∈L
if and only if v lies on a.
Given a plane P with point-set V and line-set L, construct the
point graph G of P. The vertex-set of G is V. Vertices
u, v ∈V are adjacent in G iff there is a line in L that contains
them both.
Given a plane P with point-set V and line-set L, construct the
line graph G of P. The vertex-set of G is L. Lines
a, b ∈L are adjacent in G iff there is a vertex in V that lies on
them both.
Labels: BoolElt Default: false
The graph of the ∓ 1 matrix H as described in
Brendan D. McKay's note "Hadamard equivalence via graph isomorphism"
(with self-loops omitted). The parameter Labels is set to
false by default, but when set to true, the vertices associated with
rows are labelled "row" and the others "col". Those labelled "row" are
those given loops in McKay's paper.
Returns the converse H of the directed graph G: if [u, v] is an edge of G then
[v, u] is an edge of H.
The nth odd graph. Vertices are (n - 1)--subsets of a (2n - 1)-set with
vertices adjacent if and only if the (n - 1)--subsets are disjoint.
The nth triangular graph. Vertices are 2-subsets of a n-set with
vertices adjacent if and only if the 2-subsets are unequal and not disjoint.
The nth square lattice graph. This is the cartesian product of
the nth complete graph with itself.
ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
Return the named graph.
Return a sequence of the three Chang graphs.
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