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.

Ontology

SUMO / GRAPH-THEORY

Class(es)

class

inheritable relation

unary function

minimal cut set fn

Coordinate term(s)

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

Type restrictions

subclass graph path MinimalCutSetFn(graph)

Axioms (4)

minimal cut set fn is internally related to cut set fn.

(relatedInternalConcept MinimalCutSetFn CutSetFn)

If graph is an instance of graph, then "the set of minimal paths that partition graph into two separate graphs" is a subclass of "the set of paths that partition graph into two separate graphs".

(=>
      (instance ?GRAPH Graph)
      (subclass
            (MinimalCutSetFn ?GRAPH)
            (CutSetFn ?GRAPH)))

if "the set of minimal paths that partition graph into two separate graphs" is equal to pathclass,
then there exists number so that for all path holds: if path is an instance of pathclass, then the length of path is number

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

There don't exist the set of paths that partition graph into two separate graphs path1,the set of minimal paths that partition graph into two separate graphs path2 so that the length of path1 is number1 and the length of path2 is number2 and number1 is less than number2.

(not
      (exists
            (?PATH1 ?PATH2)
            (and
                  (instance
                        ?PATH1
                        (CutSetFn ?GRAPH))
                  (instance
                        ?PATH2
                        (MinimalCutSetFn ?GRAPH))
                  (pathLength ?PATH1 ?NUMBER1)
                  (pathLength ?PATH2 ?NUMBER2)
                  (lessThan ?NUMBER1 ?NUMBER2))))