From 68d53c01b0b8e9a007a6a30158c19e34b2d2a34e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Bj=C3=B6rn=20Gustavsson?= The This module provides a version of labeled
+ directed graphs. What makes the graphs provided here
non-proper directed graphs is that multiple edges between
vertices are allowed. However, the customary definition of
- directed graphs will be used in the text that follows.
- A Digraphs can be annotated with additional information. Such
- information may be attached to the vertices and to the edges of
- the digraph. A digraph which has been annotated is called a
- labeled digraph, and the information attached to a
- vertex or an edge is called a An edge e = (v, w) is said to
-
A
In this module, V is allowed to be empty. The so obtained unique
+ digraph is called the
+
Digraphs can be annotated with more information. Such information
+ can be attached to the vertices and to the edges of the digraph. An
+ annotated digraph is called a labeled digraph, and the
+ information attached to a vertex or an edge is called a
+
An edge e = (v, w) is said to
+
The
The
If an edge is emanating from v and incident on w, then w is
+ said to be an
A
The
Path P is
Path P is a
A
A
An
A digraph as returned by
A digraph as returned by
+
If the edge would create a cycle in
- an
If the edge would create a cycle in
+ an
Deletes the edge
Deletes edge
Deletes the edges in the list
Deletes the edges in list
Deletes edges from the digraph
A sketch of the procedure employed: Find an arbitrary
-
Deletes edges from digraph
A sketch of the procedure employed:
+Find an arbitrary
+
Remove all edges of
Repeat until there is no path between
Deletes the vertex
Deletes vertex
Deletes the vertices in the list
Deletes the vertices in list
Deletes the digraph
Deletes digraph
Returns
Returns
+
Returns a list of all edges of the digraph
Returns a list of all edges of digraph
Returns a list of all
- edges
Returns a list of all
+ edges
If there is
- a
If a
Tries to find
- a
The digraph
Tries to find
+ a
Digraph
Tries to find an as short as
- possible
Tries to find an as short as possible
+
Tries to find an as short as
- possible
The digraph
Tries to find an as short as possible
+
Digraph
Returns the
Returns the
Returns a list of all
- edges
Returns a list of all
+ edges
Returns a list of
- all
Returns a list of
+ all
Returns a list of
Returns a list of
Equivalent to
Equivalent to
Returns
- an
Returns
+ an
Allows
The digraph is to be kept
+
Other processes can read the digraph (default).
The digraph can be read and modified by the creating + process only.
If an unrecognized type option
If an unrecognized type option
Returns the number of edges of the digraph
Returns the number of edges of digraph
Returns the number of vertices of the digraph
Returns the number of vertices of digraph
Returns the
Returns the
Returns a list of all
- edges
Returns a list of all
+ edges
Returns a list of
- all
Returns
Returns
Returns a list of all vertices of the digraph
Returns a list of all vertices of digraph