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圖 (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)

[tree]
實體
is subclass of
  抽象的  
is subclass of
  圖  

Subclass(es)

有向圖  樹狀圖  多圖  擬圖 

Coordinate term(s)

屬性  圖元件  命題  數量  關係  集合或種類 

Constrains relations

相交路徑函數  最小相交路徑函數  圖部分  次圖 

Related WordNet synsets

See more related synsets on a separate page.

Axioms (5)

If graph 是 圖 的 實例 and node1 是 圖節點 的 實例 and node2 是 圖節點 的 實例 and node1 是 graph 的 部分 and node2 是 graph 的 部分 and node1 等於 node2, then there exist arc,path so that 
(=>
      (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 是 圖 的 實例, then there exist node1,node2,node3,arc1,arc2 so that node1 是 graph 的 部分 and node2 是 graph 的 部分 and node3 是 graph 的 部分 and arc1 是 graph 的 部分 and arc2 是 graph 的 部分 and node2 (沒) 連結not(s) arc1 和 node1 and node3 (沒) 連結not(s) arc2 和 node2 and node1 等於 node2 and node2 等於 node3 and node1 等於 node3 and arc1 等於 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)))))
圖元件 無交集 於 圖. 
(disjoint GraphElement Graph)
If part 是 圖元件 的 實例, then there exists 圖 graph so that part 是 graph 的 部分. 
(=>
      (instance ?PART GraphElement)
      (exists
            (?GRAPH)
            (and
                  (instance ?GRAPH Graph)
                  (graphPart ?PART ?GRAPH))))
If graph 是 圖 的 實例, then "劃分 graph 為 兩 獨立 圖表 的 最小相交路�|" 是 "劃分 graph 為 兩 獨立 圖表 的 相交路�|" 的 次種類. 
(=>
      (instance ?GRAPH Graph)
      (subclass
            (MinimalCutSetFn ?GRAPH)
            (CutSetFn ?GRAPH)))