aalekha patha (GraphPath)

Informally, a single, directed route between two GraphNodes in a Graph. Formally, a DirectedGraph that is a subGraph of the original Graph and such that no two GraphArcs in the DirectedGraph have the same intial node (see InitialNodeFn) or the same terminal node (see TerminalNodeFn).

Ontology

SUMO / GRAPH-THEORY

Superclass(es)

astitva

amUrta

aalekha

pratyaksha aalekha

aalekha patha

Subclass(es)

aalekha paripatha

Constrains relations

begin node fn cut set fn end node fn graph path fn maximal weighted path fn minimal cut set fn minimal weighted path fn path weight fn path length

Related WordNet synsets

See more related synsets on a separate page.

Axioms (3)

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 patha aur arc is an instance of chaapa aalekha aur arc is a part of graph,
to agar "the starting node of arc" is equal to node, to yah kuch other nahin, ki "the starting node of other" is equal to node aur other is not equal to arc

(=>
      (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)))))))

agar graph is an instance of aalekha patha aur arc is an instance of chaapa aalekha aur arc is a part of graph,
to agar "the terminal node of arc" is equal to node, to yah kuch other nahin, ki "the terminal node of other" is equal to node aur other is not equal to 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)))))))