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# hrana grafu (GraphArc)

Graphs are comprised of GraphNodes and GraphArcs. Every GraphArc links two GraphNodes.

## Ontologie

SUMO / GRAPH-THEORY

 entita

abstraktum

prvek grafu

hrana grafu

smyčka grafu

uzel grafu

## Constrains relations

initial node fn  terminal node fn  arc weight  links

## Related WordNet synsets

See more related synsets on a separate page.

## Axiomy (5)

Jestliže graph je instancí třídy orientovaný graf a arc je instancí třídy hrana grafu a arc je částí graph, potom existují node1,node2 tak, že "initial node fn(arc)" se rovná node1 a "terminal node fn(arc)" se rovná node2.
```(=>
(and
(instance ?GRAPH DirectedGraph)
(instance ?ARC GraphArc)
(graphPart ?ARC ?GRAPH))
(exists
(?NODE1 ?NODE2)
(and
(equal
(InitialNodeFn ?ARC)
?NODE1)
(equal
(TerminalNodeFn ?ARC)
?NODE2))))```

```(=>
(and
(instance ?GRAPH GraphPath)
(instance ?ARC GraphArc)
(graphPart ?ARC ?GRAPH))
(=>
(equal
(InitialNodeFn ?ARC)
?NODE)
(not
(exists
(?OTHER)
(and
(equal
(InitialNodeFn ?OTHER)
?NODE)
(not
(equal ?OTHER ?ARC)))))))```

```(=>
(and
(instance ?GRAPH GraphPath)
(instance ?ARC GraphArc)
(graphPart ?ARC ?GRAPH))
(=>
(equal
(TerminalNodeFn ?ARC)
?NODE)
(not
(exists
(?OTHER)
(and
(equal
(TerminalNodeFn ?OTHER)
?NODE)
(not
(equal ?OTHER ?ARC)))))))```

prvek grafu je exhaustively partitioned into uzel grafu,hrana grafu.
`(partition GraphElement GraphNode GraphArc)`

Jestliže arc je instancí třídy hrana grafu, potom existují node1,node2 tak, že arc spojuje node1 a node2.
```(=>
(instance ?ARC GraphArc)
(exists
(?NODE1 ?NODE2)