aalekha (Graph)

The Class of graphs, where a graph is understood to be a set of GraphNodes connected by GraphArcs. Note that this Class includes only connected graphs, i.e. graphs in which there is a GraphPath between any two GraphNodes. Note too that every Graph is assumed to contain at least two GraphArcs and three GraphNodes.

Ontology

SUMO / GRAPH-THEORY

Superclass(es)

astitva

amUrta

aalekha

Subclass(es)

pratyaksha aalekha vriksha bahu aalekha aabhaasii aalekha

Coordinate term(s)

visheshtaa tatva aalekha prastaava parimaaNa sambandha samUha yaa varga

Constrains relations

cut set fn minimal cut set fn graph part sub graph

Related WordNet synsets

See more related synsets on a separate page.

Axioms (5)

Agar graph is an instance of aalekha aur node1 is an instance of granthi aalekha aur node2 is an instance of granthi aalekha aur node1 is a part of graph aur node2 is a part of graph aur node1 is not equal to node2, to yah kuch arc,path nahin, ki

arc links node1 and node2
- path is a subgraph of graph
- path is an instance of aalekha patha
- - "the beginning of path" is equal to node1 aur "the end of path" is equal to node2
  - "the beginning of path" is equal to node2 aur "the end of path" is equal to node1

(=>
      (and
            (instance ?GRAPH Graph)
            (instance ?NODE1 GraphNode)
            (instance ?NODE2 GraphNode)
            (graphPart ?NODE1 ?GRAPH)
            (graphPart ?NODE2 ?GRAPH)
            (not
                  (equal ?NODE1 ?NODE2)))
      (exists
            (?ARC ?PATH)
            (or
                  (links ?NODE1 ?NODE2 ?ARC)
                  (and
                        (subGraph ?PATH ?GRAPH)
                        (instance ?PATH GraphPath)
                        (or
                              (and
                                    (equal
                                          (BeginNodeFn ?PATH)
                                          ?NODE1)
                                    (equal
                                          (EndNodeFn ?PATH)
                                          ?NODE2))
                              (and
                                    (equal
                                          (BeginNodeFn ?PATH)
                                          ?NODE2)
                                    (equal
                                          (EndNodeFn ?PATH)
                                          ?NODE1)))))))

Agar graph is an instance of aalekha, to yah kuch node1,node2,node3,arc1,arc2 nahin, ki node1 is a part of graph aur node2 is a part of graph aur node3 is a part of graph aur arc1 is a part of graph aur arc2 is a part of graph aur node2 links arc1 and node1 aur node3 links arc2 and node2 aur node1 is not equal to node2 aur node2 is not equal to node3 aur node1 is not equal to node3 aur arc1 is not equal to arc2.

(=>
      (instance ?GRAPH Graph)
      (exists
            (?NODE1 ?NODE2 ?NODE3 ?ARC1 ?ARC2)
            (and
                  (graphPart ?NODE1 ?GRAPH)
                  (graphPart ?NODE2 ?GRAPH)
                  (graphPart ?NODE3 ?GRAPH)
                  (graphPart ?ARC1 ?GRAPH)
                  (graphPart ?ARC2 ?GRAPH)
                  (links ?ARC1 ?NODE1 ?NODE2)
                  (links ?ARC2 ?NODE2 ?NODE3)
                  (not
                        (equal ?NODE1 ?NODE2))
                  (not
                        (equal ?NODE2 ?NODE3))
                  (not
                        (equal ?NODE1 ?NODE3))
                  (not
                        (equal ?ARC1 ?ARC2)))))

tatva aalekha asansavat aalekha se hai.

(disjoint GraphElement Graph)

Agar part is an instance of tatva aalekha, to yah kuch aalekha graph nahin, ki part is a part of graph.

(=>
      (instance ?PART GraphElement)
      (exists
            (?GRAPH)
            (and
                  (instance ?GRAPH Graph)
                  (graphPart ?PART ?GRAPH))))

Agar graph is an instance of aalekha, to "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)))