tu2 (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)

shi2 ti3

chou1 xiang4 de5

tu2

Subclass(es)

you3 xiang4 tu2 shu4 zhuang4 tu2 duo1 tu2 ni3 tu2

Coordinate term(s)

shu3 xing4 tu2 yuan2 jian4 ming4 ti2 shu4 liang4 guan1 xi4 ji2 he2 huo4 zhong3 lei4

Constrains relations

xiang1 jiao1 lu4 jing4 han2 shu4 zui4 xiao3 xiang1 jiao1 lu4 jing4 han2 shu4 tu2 bu4 fen5 ci4 tu2

Related WordNet synsets

See more related synsets on a separate page.

Axioms (5)

If graph shi4 tu2 de5 shi2 li4 and node1 shi4 tu2 jie2 dian3 de5 shi2 li4 and node2 shi4 tu2 jie2 dian3 de5 shi2 li4 and node1 shi4 graph de5 bu4 fen5 and node2 shi4 graph de5 bu4 fen5 and node1 deng3 yu1 node2, then there exist arc,path so_that_not

arc (mei2) lian2 jie2not(s) node1 he2 node2
- path shi4 graph de5 ci4 tu2
- path shi4 tu2 lu4 jing4 de5 shi2 li4
- - "path de5 zui4 chu1 jie2 dian3" deng3 yu1 node1 and "path de5 zui4 hou4 jie2 dian3" deng3 yu1 node2
  - "path de5 zui4 chu1 jie2 dian3" deng3 yu1 node2 and "path de5 zui4 hou4 jie2 dian3" deng3 yu1 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)))))))

If graph shi4 tu2 de5 shi2 li4, then there exist node1,node2,node3,arc1,arc2 so_that_not node1 shi4 graph de5 bu4 fen5 and node2 shi4 graph de5 bu4 fen5 and node3 shi4 graph de5 bu4 fen5 and arc1 shi4 graph de5 bu4 fen5 and arc2 shi4 graph de5 bu4 fen5 and node2 (mei2) lian2 jie2not(s) arc1 he2 node1 and node3 (mei2) lian2 jie2not(s) arc2 he2 node2 and node1 deng3 yu1 node2 and node2 deng3 yu1 node3 and node1 deng3 yu1 node3 and arc1 deng3 yu1 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)))))

tu2 yuan2 jian4 wu2 jiao1 ji2 yu1 tu2.

(disjoint GraphElement Graph)

If part shi4 tu2 yuan2 jian4 de5 shi2 li4, then there exists tu2 graph so_that_not part shi4 graph de5 bu4 fen5.

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

If graph shi4 tu2 de5 shi2 li4, then "hua2 fen1 graph wei2 liang3 du2 li4 tu2 biao3 de5 zui4 xiao3 xiang1 jiao1 lu4 jing4" shi4 "hua2 fen1 graph wei2 liang3 du2 li4 tu2 biao3 de5 xiang1 jiao1 lu4 jing4" de5 ci4 zhong3 lei4.

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