Identifier
Values
=>
Cc0020;cc-rep-2 Cc0020;cc-rep
[1]=>[1]=>([],1)=>([],1)=>1 [1,2]=>[1,2]=>([],2)=>([],1)=>1 [2,1]=>[1,2]=>([],2)=>([],1)=>1 [1,2,3]=>[1,2,3]=>([],3)=>([],1)=>1 [1,3,2]=>[1,2,3]=>([],3)=>([],1)=>1 [2,1,3]=>[1,2,3]=>([],3)=>([],1)=>1 [2,3,1]=>[1,2,3]=>([],3)=>([],1)=>1 [1,2,3,4]=>[1,2,3,4]=>([],4)=>([],1)=>1 [1,2,4,3]=>[1,2,3,4]=>([],4)=>([],1)=>1 [1,3,2,4]=>[1,2,3,4]=>([],4)=>([],1)=>1 [1,3,4,2]=>[1,2,3,4]=>([],4)=>([],1)=>1 [2,1,3,4]=>[1,2,3,4]=>([],4)=>([],1)=>1 [2,1,4,3]=>[1,2,3,4]=>([],4)=>([],1)=>1 [2,3,1,4]=>[1,2,3,4]=>([],4)=>([],1)=>1 [2,3,4,1]=>[1,2,3,4]=>([],4)=>([],1)=>1 [1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,2,3,5,4]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,2,4,3,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,2,4,5,3]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,3,2,4,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,3,2,5,4]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,3,4,2,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,3,4,5,2]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,1,3,4,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,1,3,5,4]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,1,4,3,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,1,4,5,3]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,3,1,4,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,3,1,5,4]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,3,4,1,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [2,3,4,5,1]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,3,4,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,3,5,4,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,3,5,6,4]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,4,3,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,4,3,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,4,5,3,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,4,5,6,3]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,2,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,2,4,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,2,5,4,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,2,5,6,4]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,4,2,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,4,2,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,4,5,2,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,3,4,5,6,2]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,3,4,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,3,5,4,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,3,5,6,4]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,4,3,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,4,3,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,4,5,3,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,1,4,5,6,3]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,1,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,1,4,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,1,5,4,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,1,5,6,4]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,4,1,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,4,1,6,5]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,4,5,1,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [2,3,4,5,6,1]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,4,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,4,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,4,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,5,4,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,5,4,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,5,6,4,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,5,6,7,4]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,3,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,3,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,3,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,3,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,5,3,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,5,3,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,5,6,3,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,4,5,6,7,3]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,4,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,4,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,4,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,5,4,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,5,4,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,5,6,4,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,2,5,6,7,4]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,2,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,2,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,2,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,2,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,5,2,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,5,2,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,5,6,2,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,3,4,5,6,7,2]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,4,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,4,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,4,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,5,4,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,5,4,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,5,6,4,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,3,5,6,7,4]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,3,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,3,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,3,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,3,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,5,3,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,5,3,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,5,6,3,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,1,4,5,6,7,3]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,4,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,4,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,4,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,5,4,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,5,4,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,5,6,4,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,1,5,6,7,4]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,1,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,1,5,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,1,6,5,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,1,6,7,5]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,5,1,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,5,1,7,6]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,5,6,1,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>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 number of distinct eigenvalues of the distance Laplacian of a connected graph.
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
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.