Identifier
Values
[.,.] => [[]] => ([(0,1)],2) => 2
[.,[.,.]] => [[[]]] => ([(0,2),(1,2)],3) => 3
[[.,.],.] => [[],[]] => ([(0,2),(1,2)],3) => 3
[.,[[.,.],.]] => [[[],[]]] => ([(0,3),(1,3),(2,3)],4) => 4
[[[.,.],.],.] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 4
[.,[[[.,.],.],.]] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 5
[[[[.,.],.],.],.] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 5
[.,[[[[.,.],.],.],.]] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6
[[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6
[.,[[[[[.,.],.],.],.],.]] => [[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 7
[[[[[[.,.],.],.],.],.],.] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 7
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 largest Laplacian eigenvalue of a graph if it is integral.
This statistic is undefined if the largest Laplacian eigenvalue of the graph is not integral.
Various results are collected in Section 3.9 of [1]
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
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 $y$.