Identifier
Values
0 => ([(0,1)],2) => ([],2) => 0
1 => ([(0,1)],2) => ([],2) => 0
00 => ([(0,2),(2,1)],3) => ([],3) => 0
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 0
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 0
11 => ([(0,2),(2,1)],3) => ([],3) => 0
000 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
111 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 0
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 0
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
Half of the Albertson index of a graph.
This is $\frac{1}{2}\sum_{\{u,v\}\in E}|d(u)-d(v)|$, where $E$ is the set of edges and $d_v$ is the degree of vertex $v$, see [1].
In particular, this statistic vanishes on graphs whose components are all regular, see [2].
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.