Identifier
Values
[.,.] => [[]] => ([(0,1)],2) => ([(0,1)],2) => 1
[.,[.,.]] => [[[]]] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 1
[[.,.],.] => [[],[]] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 1
[.,[.,[.,.]]] => [[[[]]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[.,.],.]] => [[[],[]]] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 1
[[.,.],[.,.]] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,.]],.] => [[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,.],.],.] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 1
[.,[.,[.,[.,.]]]] => [[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[.,[[.,.],.]]] => [[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[.,.],[.,.]]] => [[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[.,[.,.]],.]] => [[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[.,.],.],.]] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 1
[[.,.],[.,[.,.]]] => [[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[.,.],[[.,.],.]] => [[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,.]],[.,.]] => [[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],.],[.,.]] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,[.,.]]],.] => [[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[.,[[.,.],.]],.] => [[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,.],[.,.]],.] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,[.,.]],.],.] => [[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,.],.],.],.] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 1
[.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[.,[.,[.,[[.,.],.]]]] => [[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[.,[[[.,.],.],.]]] => [[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[.,[.,[.,.]]],.]] => [[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[.,[.,.]],.],.]] => [[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[[.,.],.],.],.]] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 1
[[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[.,[[.,.],.]]],.] => [[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[.,[[[.,.],.],.]],.] => [[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,[[.,.],.]],.],.] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,[.,.]],.],.],.] => [[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [[[[[[],[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[.,[.,[.,[[[.,.],.],.]]]] => [[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[.,[[[[.,.],.],.],.]]] => [[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [[[[[[]]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[.,[[.,[.,[[.,.],.]]],.]] => [[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[[.,[[[.,.],.],.]],.]] => [[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[.,[.,[.,.]]],.],.]] => [[[[[]]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[.,[[[.,[[.,.],.]],.],.]] => [[[[],[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[[.,.],[.,.]],.],.]] => [[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[[.,[.,.]],.],.],.]] => [[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[.,[[[[[.,.],.],.],.],.]] => [[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,[.,[[.,.],.]]]],.] => [[[[[],[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[.,[[[.,.],.],.]]],.] => [[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[.,[[[[.,.],.],.],.]],.] => [[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,[.,[.,[.,.]]]],.],.] => [[[[[]]]],[],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[.,[.,[[.,.],.]]],.],.] => [[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
>>> Load all 110 entries. <<<
[[[.,[[[.,.],.],.]],.],.] => [[[],[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[.,.],[[.,.],.]],.],.] => [[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,[.,[.,.]]],.],.],.] => [[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[.,[[.,.],.]],.],.],.] => [[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[[.,[.,.]],.],.],.],.] => [[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 1
[[[[[[.,.],.],.],.],.],.] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The Colin de Verdière graph invariant.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
  • if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.