Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001362
Mapping
St001362: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 1
([],3)
 => 0
([(1,2)],3)
 => 2
([(0,2),(1,2)],3)
 => 3
([(0,1),(0,2),(1,2)],3)
 => 6
([],4)
 => 0
([(2,3)],4)
 => 6
([(1,3),(2,3)],4)
 => 9
([(0,3),(1,3),(2,3)],4)
 => 12
([(0,3),(1,2)],4)
 => 12
([(0,3),(1,2),(2,3)],4)
 => 12
([(1,2),(1,3),(2,3)],4)
 => 18
([(0,3),(1,2),(1,3),(2,3)],4)
 => 20
([(0,2),(0,3),(1,2),(1,3)],4)
 => 12
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 24
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 36
([],5)
 => 0
([(3,4)],5)
 => 24
([(2,4),(3,4)],5)
 => 36
([(1,4),(2,4),(3,4)],5)
 => 48
([(0,4),(1,4),(2,4),(3,4)],5)
 => 60
([(1,4),(2,3)],5)
 => 48
([(1,4),(2,3),(3,4)],5)
 => 48
([(0,1),(2,4),(3,4)],5)
 => 60
([(2,3),(2,4),(3,4)],5)
 => 72
([(0,4),(1,4),(2,3),(3,4)],5)
 => 60
([(1,4),(2,3),(2,4),(3,4)],5)
 => 80
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 90
([(1,3),(1,4),(2,3),(2,4)],5)
 => 48
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 60
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 96
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 88
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 105
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 60
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 120
([(0,4),(1,3),(2,3),(2,4)],5)
 => 60
([(0,1),(2,3),(2,4),(3,4)],5)
 => 96
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 92
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 120
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 60
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 88
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 120
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 104
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 144
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 150
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 160
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 100
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 120
Description
The normalized Knill dimension of a graph. The Knill dimension [1], [2] is a rational number associated with a graph as follows: for the empty graph $\dim(G) = -1$. For a graph with non-empty vertex set $V$, it is $\dim(G) = 1 + \frac{1}{|V|}\sum_{v\in V}\dim(N_v)$, where $N_v$ is the subgraph of $G$ induced by the set of neighbours of $v$. Conjecturally, the least common multiple of the denominators of all graphs is the order of the alternating group [[oeis:A001710]]. Thus, the normalized Knill dimension is the Knill dimension multiplied with the number.