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# minimal cut set fn (MinimalCutSetFn)

A UnaryFunction that assigns a Graph the Class of GraphPaths which comprise cutsets for the Graph and which have the least number of GraphArcs.

## Ontologie

SUMO / GRAPH-THEORY

## Class(es)

 třída

inheritable relation

unární funkce

minimal cut set fn

## Související termín(y)

absolute value fn  abstraction fn  arc cosine fn  arc sine fn  arc tangent fn  back fn  begin fn  begin node fn  cardinality fn  ceiling fn  complement fn  cosine fn  cut set fn  denominator fn  end fn  end node fn  extension fn  floor fn  front fn  future fn  generalized intersection fn  generalized union fn  giga fn  imaginary part fn  immediate future fn  immediate past fn  initial node fn  integer square root fn  kilo fn  list length fn  magnitude fn  mega fn  micro fn  milli fn  nano fn  numerator fn  organization fn  past fn  path weight fn  pico fn  power set fn  predecessor fn  principal host fn  probability fn  property fn  rational number fn  real number fn  reciprocal fn  round fn  signum fn  sine fn  skin fn  square root fn  successor fn  tangent fn  tera fn  terminal node fn  wealth fn  when fn  year fn

## Typy argumentů

subclass cesta v grafu MinimalCutSetFn(graf)

## Axiomy (4)

minimal cut set fn je internally related to cut set fn.
`(relatedInternalConcept MinimalCutSetFn CutSetFn)`

Jestliže graph je instancí třídy graf, potom "minimal cut set fn(graph)" je podtřídou "cut set fn(graph)".
```(=>
(instance ?GRAPH Graph)
(subclass
(MinimalCutSetFn ?GRAPH)
(CutSetFn ?GRAPH)))```

```(=>
(equal
(MinimalCutSetFn ?GRAPH)
?PATHCLASS)
(exists
(?NUMBER)
(forall
(?PATH)
(=>
(instance ?PATH ?PATHCLASS)
(pathLength ?PATH ?NUMBER)))))```

Neexistují cut set fn(graph) path1,minimal cut set fn(graph) path2 tak, že délka path1 je number1 a délka path2 je number2 a number1 je menší než number2.
```(not
(exists
(?PATH1 ?PATH2)
(and
(instance
?PATH1
(CutSetFn ?GRAPH))
(instance
?PATH2
(MinimalCutSetFn ?GRAPH))
(pathLength ?PATH1 ?NUMBER1)
(pathLength ?PATH2 ?NUMBER2)
(lessThan ?NUMBER1 ?NUMBER2))))```