Identifier
Values
[.,.] => [[],[]] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 0
[.,[.,.]] => [[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[.,.],.] => [[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[.,[.,[.,.]]] => [[],[[],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[.,[[.,.],.]] => [[],[[[],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[.,.],[.,.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[[.,[.,.]],.] => [[[],[[],[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[.,.],.],.] => [[[[],[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 6
[[.,.],[.,[.,.]]] => [[[],[]],[[],[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 6
[[.,.],[[.,.],.]] => [[[],[]],[[[],[]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 6
[[.,[.,.]],[.,.]] => [[[],[[],[]]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 6
[[[.,.],.],[.,.]] => [[[[],[]],[]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 6
[[[.,.],[.,.]],.] => [[[[],[]],[[],[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 6
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Description
The number of pairs of vertices of a graph with distance 2.
This is the coefficient of the quadratic term of the Wiener polynomial.
Map
to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
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.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.