Identifier
Values
[.,.] => ([],1) => ([],1) => 0
[.,[.,.]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[.,.],.] => ([(0,1)],2) => ([(0,1)],2) => 0
[.,[.,[.,.]]] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 0
[.,[[.,.],.]] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 0
[[.,.],[.,.]] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 0
[[.,[.,.]],.] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 0
[[[.,.],.],.] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 0
[.,[.,[.,[.,.]]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[.,[.,[[.,.],.]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[.,[[.,.],[.,.]]] => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[.,[[.,[.,.]],.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[.,[[[.,.],.],.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[.,[.,[.,.]]],.] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[.,[[.,.],.]],.] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[[.,.],[.,.]],.] => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[[[.,[.,.]],.],.] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[[[[.,.],.],.],.] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
[.,[.,[.,[.,[.,.]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[.,[.,[[.,.],.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[.,[.,[[.,[.,.]],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[.,[[[.,.],.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[.,[[.,.],[[.,.],.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[.,[[[.,.],.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[.,[[.,[.,[.,.]]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[[.,[[.,.],.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[.,[[[.,[.,.]],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[[[[.,.],.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,.],[.,[[.,.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[.,.],[[.,[.,.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,.],[[[.,.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[.,.]],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[.,.]],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[.,.],.],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[[.,.],.]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[.,[.,.]],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[.,[.,[.,.]]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[.,[[.,.],.]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[.,[[.,[.,.]],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[.,[[[.,.],.],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[.,.],[.,[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[.,.],[[.,.],.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[.,[.,.]],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[[.,.],.],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[.,[.,[.,.]]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[.,[[.,.],.]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[[.,[.,.]],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[[[.,.],.],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[.,[[[.,.],[.,.]],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[[.,.],[.,.]],[.,.]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[[.,[[.,.],[.,.]]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
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Description
The number of triconnected components of a graph.
A connected graph is triconnected or 3-vertex connected if it cannot be disconnected by removing two or fewer vertices. An arbitrary connected graph can be decomposed as a union of biconnected (2-vertex connected) graphs, known as blocks, and each biconnected graph can be decomposed as a union of components with are either a cycle (type "S"), a cocyle (type "P"), or triconnected (type "R"). The decomposition of a biconnected graph into these components is known as the SPQR-tree of the graph.
A connected graph is triconnected or 3-vertex connected if it cannot be disconnected by removing two or fewer vertices. An arbitrary connected graph can be decomposed as a union of biconnected (2-vertex connected) graphs, known as blocks, and each biconnected graph can be decomposed as a union of components with are either a cycle (type "S"), a cocyle (type "P"), or triconnected (type "R"). The decomposition of a biconnected graph into these components is known as the SPQR-tree of the graph.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
Map
square
Description
The square of a graph.
For a graph G, the square is the graph on the same set of vertices where two vertices are joined by an edge if there is a path in G of length at most two between the two.
In other words, a vertex gets joint to its 2-neighbourhood in G.
For a graph G, the square is the graph on the same set of vertices where two vertices are joined by an edge if there is a path in G of length at most two between the two.
In other words, a vertex gets joint to its 2-neighbourhood in G.
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