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, and a non-negative integer n, return the set of
all vertices of G that have degree equal to n.
Maxdeg(G) : GrphUnd -> RngIntElt, GrphVert
The maximum of the degrees of the vertices of the graph 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 the graph G. This function
returns two values: the minimum degree, and a vertex of G having
that degree.
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 a regular graph G, return the valence of G (the degree of
any vertex).
Neighbors(u) : GrphVert -> { GrphVert }
Given a vertex u of the graph G, return the set of vertices of
G that are adjacent to u.
The set of all edges incident with the vertex u.
Given a bipartite graph G, return its two partite sets in the form
of a pair of subsets of V(G).
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).
The number of edges directed into the vertex u belonging to the
directed graph G.
The number of edges of the form uv where u is a vertex belonging
to the directed graph G.
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 a digraph G, and a non--negative integer n, return the set
of all vertices of G that have total degree equal to n.
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.
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.
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.
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.
Given a digraph 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.
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.
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.
The set of all edges incident with the vertex u.
V2.28, 13 July 2023