Values
=>
Cc0020;cc-rep
([],0)=>1
([],1)=>2
([],2)=>4
([(0,1)],2)=>4
([],3)=>8
([(1,2)],3)=>8
([(0,2),(1,2)],3)=>7
([(0,1),(0,2),(1,2)],3)=>5
([],4)=>16
([(2,3)],4)=>16
([(1,3),(2,3)],4)=>14
([(0,3),(1,3),(2,3)],4)=>12
([(0,3),(1,2)],4)=>16
([(0,3),(1,2),(2,3)],4)=>12
([(1,2),(1,3),(2,3)],4)=>10
([(0,3),(1,2),(1,3),(2,3)],4)=>8
([(0,2),(0,3),(1,2),(1,3)],4)=>10
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>6
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>6
([],5)=>32
([(3,4)],5)=>32
([(2,4),(3,4)],5)=>28
([(1,4),(2,4),(3,4)],5)=>24
([(0,4),(1,4),(2,4),(3,4)],5)=>21
([(1,4),(2,3)],5)=>32
([(1,4),(2,3),(3,4)],5)=>24
([(0,1),(2,4),(3,4)],5)=>28
([(2,3),(2,4),(3,4)],5)=>20
([(0,4),(1,4),(2,3),(3,4)],5)=>20
([(1,4),(2,3),(2,4),(3,4)],5)=>16
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>13
([(1,3),(1,4),(2,3),(2,4)],5)=>20
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>16
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>12
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>13
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>9
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>13
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7
([(0,4),(1,3),(2,3),(2,4)],5)=>21
([(0,1),(2,3),(2,4),(3,4)],5)=>20
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>14
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>9
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>17
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>11
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>7
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>10
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>12
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>9
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>7
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7
([],6)=>64
([(4,5)],6)=>64
([(3,5),(4,5)],6)=>56
([(2,5),(3,5),(4,5)],6)=>48
([(1,5),(2,5),(3,5),(4,5)],6)=>42
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>38
([(2,5),(3,4)],6)=>64
([(2,5),(3,4),(4,5)],6)=>48
([(1,2),(3,5),(4,5)],6)=>56
([(3,4),(3,5),(4,5)],6)=>40
([(1,5),(2,5),(3,4),(4,5)],6)=>40
([(0,1),(2,5),(3,5),(4,5)],6)=>48
([(2,5),(3,4),(3,5),(4,5)],6)=>32
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>34
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>26
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>22
([(2,4),(2,5),(3,4),(3,5)],6)=>40
([(0,5),(1,5),(2,4),(3,4)],6)=>49
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>32
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>35
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>24
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>26
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>33
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>26
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>18
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>21
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>26
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>26
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>20
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>16
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,5),(1,4),(2,3)],6)=>64
([(1,5),(2,4),(3,4),(3,5)],6)=>42
([(0,1),(2,5),(3,4),(4,5)],6)=>48
([(1,2),(3,4),(3,5),(4,5)],6)=>40
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>34
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>28
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>32
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>22
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>18
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>14
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>34
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>25
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>22
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>28
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>20
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>22
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>17
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>37
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>40
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>35
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>28
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>25
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>23
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>24
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>23
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>18
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>16
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>24
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>16
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>18
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>22
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>14
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>11
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>14
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>20
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>18
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>13
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>14
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>29
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>21
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>18
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>19
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>18
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>18
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>13
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>12
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>12
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>8
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>17
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>16
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>12
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>8
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>17
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>10
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>25
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>18
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>17
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>24
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>12
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>16
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>13
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>10
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>8
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>15
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>14
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>10
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>13
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>8
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>14
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>8
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>10
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>8
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>8
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
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Description
The number of closed sets in a graph.
A subset $S$ of the set of vertices is a closed set, if for any pair of distinct elements of $S$ the intersection of the corresponding neighbourhoods is a subset of $S$:
$$ \forall a, b\in S: N(a)\cap N(b) \subseteq S. $$
A subset $S$ of the set of vertices is a closed set, if for any pair of distinct elements of $S$ the intersection of the corresponding neighbourhoods is a subset of $S$:
$$ \forall a, b\in S: N(a)\cap N(b) \subseteq S. $$
References
[1] Koh, K. M., Poh, K. S. On the spectrum of the closed-set lattice of a graph MathSciNet:1165806
Code
def is_closed_set(G, S):
for u, v in Subsets(S, 2):
if not set(G[u]).intersection(G[v]).issubset(S):
return False
return True
def statistic(G):
return sum(1 for S in Subsets(G.vertices()) if is_closed_set(G, S))
Created
Mar 31, 2021 at 21:51 by Martin Rubey
Updated
Mar 31, 2021 at 21:51 by Martin Rubey
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