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Subsections
Given a graph G, and a non-negative integer n, return the set of
all vertices of G that have degree equal to n.
Given a vertex u belonging to a graph G, and a non-negative
integer n, return the set of vertices of G that are at distance
n or less from u.
Given a bipartite graph G, return its two partite sets in the form
of a pair of subsets of V(G).
Given a vertex u of the graph G, return the degree of u, ie
the number of edges incident to u.
Given a graph G such that the maximum degree of any vertex of G
is r, return a sequence D of length r + 1, such that D[i],
1 <= i <= r + 1, is the number of vertices in G having
degree i - 1.
Given two vertices u and v belonging to a graph G, return the
length of a shortest path from u to v. If u and v lie in
different components, the value -1 is returned.
Given an edge e belonging to the graph G, return a set
containing the two end vertices of e.
The set of all edges incident with the vertex u.
Maxdeg(G) : GrphUnd -> RngIntElt, GrphVert
The maximum of the degrees of the vertices of G. This function
returns two values: The maximum degree, and a vertex of G having
that degree.
Mindeg(G) : GrphUnd -> RngIntElt, GrphVert
The minimum of the degrees of the vertices of G. This function
returns two values: The minimum degree, and a vertex of G having
that degree.
Neighbors(u) : GrphVert -> { GrphVert }
Given a vertex u of the graph G, return the set of vertices of
G that are adjacent to u.
Given a vertex u belonging to the graph G, and a non-negative
integer n, return the set of vertices of G that are at distance
n from u.
Given a regular graph G, return the valence of G (the degree of
any vertex).
A dominating set S of a graph G is such that the vertices of S
together with the vertices adjacent to vertices
in S form the vertex set of G.
A dominating set S is minimal if no proper subset of S is
a dominating set.
A minimum dominating set is a minimal dominating set
of smallest size.
The algorithm implemented is a backtrack algorithm (see [Chr75] p. 41).
Given vertices u and v belonging to a digraph G, return the
value true if there is an edge directed from vertex u to vertex v,
otherwise false.
Returns true if the edge e is adjacent to the edge f, where e and f
are edges belonging to the digraph G, otherwise false.
Given vertices u and v belonging to a digraph G, return the
value true if there is not an edge directed from vertex u to vertex v,
otherwise false.
Returns true if the edge e is not adjacent to the edge f, where e and f
are edges belonging to the digraph G, otherwise false.
Returns true if the vertex u is an endpoint of the edge e, where u and
e belong to the digraph G, otherwise false.
Given a digraph G, and a non--negative integer n, return the set
of all vertices of G that have total degree equal to n.
Given a vertex u belonging to a connected digraph G, and a
non--negative integer n, return the set of vertices of G that
are at distance n or less from u. Thus, Ball(u, n) is
the set of vertices of G that are connected to u by a directed
path of length at most n.
Given a vertex u belonging to the digraph G, return the total
degree of u, i.e. the sum of the in--degree and out--degree for u.
Given an edge e belonging to the digraph G, return a sequence of
length two whose first component is the first vertex of e, and whose
second component is the second vertex of e.
The number of edges directed into the vertex u belonging to the
directed graph G.
InNeighbors(u) : GrphVert -> { GrphVert }
Given a vertex u of the digraph G, return the set containing all
vertices v such that vu is an edge in the digraph, i.e. the starting
points of all edges that are directed into the vertex u.
Maxdeg(G) : GrphDir -> RngIntElt, GrphVert
The maximum total degree of the vertices of the digraph G. This
function returns two values: The maximum total degree, and the first
vertex of G having that degree.
Maxindeg(G) : GrphDir -> RngIntElt, GrphVert
The maximum indegree of the vertices of the digraph G. This function
returns two values: The maximum indegree, and the first vertex
of G having that degree.
Maxoutdeg(G) : GrphDir -> RngIntElt, GrphVert
The maximum outdegree of the vertices of the digraph G. This function
returns two values: The maximum outdegree, and the first vertex of G
having that degree.
Mindeg(G) : GrphDir -> RngIntElt, GrphVert
The minimum total degree of the vertices of the digraph G. This
function returns two values: The minimum total degree, and the first
vertex of G having that degree.
Minindeg(G) : GrphDir -> RngIntElt, GrphVert
The minimum indegree of the vertices of the digraph G. This function
returns two values: The minimum indegree, and the first vertex of G
having that degree.
Minoutdeg(G) : GrphDir -> RngIntElt, GrphVert
The minimum outdegree of the vertices of the digraph G. This function
returns two values: The minimum outdegree, and the first vertex of G
having that degree.
The number of edges of the form uv where u is a vertex belonging
to the directed graph G.
OutNeighbors(u) : GrphVert -> { GrphVert }
Given a vertex u of the digraph G, return the set of vertices v
of G such that uv is an edge in the graph G, i.e. the set of
vertices v that are the end vertices of edges directed from u to
v.
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