OpenMath Content Dictionary: graph3

Canonical URL:
http://www.openmath.org/cd/graph3.ocd
CD Base:
http://www.openmath.org/cd
CD File:
graph3.ocd
CD as XML Encoded OpenMath:
graph3.omcd
Defines:
labelledgraph, mixedgraph
Date:
2018-12-28
Version:
0 (Revision 2)
Review Date:
2019-01-05
Status:
experimental

    Author: Wouter Termont
    SourceURL: https://github.com/OpenMath/CDs
            
     This document is distributed in the hope that it will be useful, 
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     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

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     provided that the following conditions are met.
       a) The derived work acknowledges the fact that it is derived from
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          work to the original source.
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          both this document and the derived work are Content Dictionaries
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          chosen so that it cannot be confused with any works adopted by
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This CD defines symbols for handling mixed graphs, multigraphs and labeled graphs. Authored by Wouter Termont. May have to be merged with the graph1 and graph2 CDs.


mixedgraph

Description:

This symbol represents a mixed graph. It takes three arguments: the vertex set of the graph, the set of undirected edges, and the set of directed edges (a.k.a. arrows or arcs). The vertices can be arbitrary OpenMath objects. Each undirected edge should be a set consisting of two vertices; each directed edge should be a list consisting of two vertices.

Example:
A simple chain graph.
mixedgraph ( { 1 , 2 , 3 } , { { 1 , 2 } } , { ( 2 , 3 ) , ( 3 , 1 ) } )
Signatures:
sts


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labelledgraph

Description:

This symbol represents a labelled (mixed) graph. It takes three arguments: the vertex set of the graph, the set of labelled undirected edges, and the set of labelled directed edges (a.k.a. arrows or arcs). Both vertices and labels can be arbitrary OpenMath objects. Each undirected edge should be a set consisting of two vertices; each directed edge should be a list consisting of two vertices.

Example:
The logical graph corresponding to a traditional Aristotelian square.
labelledgraph ( { A , E , I , O } , { Pair ( { A , E } , C ) , Pair ( { A , O } , CD ) , Pair ( { E , I } , CD ) , Pair ( { I , O } , SC ) } , { Pair ( ( A , I ) , SA ) , Pair ( ( E , O ) , SA ) } )
Signatures:
sts


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