Identifier
-
Mp00011:
Binary trees
—to graph⟶
Graphs
St000095: Graphs ⟶ ℤ
Values
[.,.] => ([],1) => 0
[.,[.,.]] => ([(0,1)],2) => 0
[[.,.],.] => ([(0,1)],2) => 0
[.,[.,[.,.]]] => ([(0,2),(1,2)],3) => 0
[.,[[.,.],.]] => ([(0,2),(1,2)],3) => 0
[[.,.],[.,.]] => ([(0,2),(1,2)],3) => 0
[[.,[.,.]],.] => ([(0,2),(1,2)],3) => 0
[[[.,.],.],.] => ([(0,2),(1,2)],3) => 0
[.,[.,[.,[.,.]]]] => ([(0,3),(1,2),(2,3)],4) => 0
[.,[.,[[.,.],.]]] => ([(0,3),(1,2),(2,3)],4) => 0
[.,[[.,.],[.,.]]] => ([(0,3),(1,3),(2,3)],4) => 0
[.,[[.,[.,.]],.]] => ([(0,3),(1,2),(2,3)],4) => 0
[.,[[[.,.],.],.]] => ([(0,3),(1,2),(2,3)],4) => 0
[[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => 0
[[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => 0
[[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 0
[[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 0
[[.,[.,[.,.]]],.] => ([(0,3),(1,2),(2,3)],4) => 0
[[.,[[.,.],.]],.] => ([(0,3),(1,2),(2,3)],4) => 0
[[[.,.],[.,.]],.] => ([(0,3),(1,3),(2,3)],4) => 0
[[[.,[.,.]],.],.] => ([(0,3),(1,2),(2,3)],4) => 0
[[[[.,.],.],.],.] => ([(0,3),(1,2),(2,3)],4) => 0
[.,[.,[.,[.,[.,.]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[.,[.,[[.,.],.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[.,[.,[[.,[.,.]],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[.,[[[.,.],.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[.,[[.,.],[[.,.],.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[.,[[[.,.],.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[.,[[.,[.,[.,.]]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[[.,[[.,.],.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[.,[[[.,[.,.]],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[[[[.,.],.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,.],[.,[[.,.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[.,.],[[.,[.,.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,.],[[[.,.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[.,.]],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[.,.]],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[.,.],.],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[[.,.],.]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[.,[.,.]],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[.,[.,[.,.]]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[.,[[.,.],.]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[.,[[.,[.,.]],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[.,[[[.,.],.],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[.,.],[.,[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[.,.],[[.,.],.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[.,[.,.]],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[[.,.],.],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[.,[.,[.,.]]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[.,[[.,.],.]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[[.,[.,.]],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[[[.,.],.],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[.,[[[.,.],[.,.]],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[[.,.],[.,.]],[.,.]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[[.,[[.,.],[.,.]]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
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Description
The number of triangles of a graph.
A triangle $T$ of a graph $G$ is a collection of three vertices $\{u,v,w\} \in G$ such that they form $K_3$, the complete graph on three vertices.
A triangle $T$ of a graph $G$ is a collection of three vertices $\{u,v,w\} \in G$ such that they form $K_3$, the complete graph on three vertices.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
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