Identifier
Identifier
Values
([],1) generating graphics... => 0
([],2) generating graphics... => 2
([(0,1)],2) generating graphics... => 1
([],3) generating graphics... => 3
([(1,2)],3) generating graphics... => 2
([(0,2),(1,2)],3) generating graphics... => 2
([(0,1),(0,2),(1,2)],3) generating graphics... => 2
([],4) generating graphics... => 3
([(2,3)],4) generating graphics... => 3
([(1,3),(2,3)],4) generating graphics... => 3
([(0,3),(1,3),(2,3)],4) generating graphics... => 3
([(0,3),(1,2)],4) generating graphics... => 4
([(0,3),(1,2),(2,3)],4) generating graphics... => 3
([(1,2),(1,3),(2,3)],4) generating graphics... => 3
([(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 2
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 4
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 3
([],5) generating graphics... => 4
([(3,4)],5) generating graphics... => 3
([(2,4),(3,4)],5) generating graphics... => 3
([(1,4),(2,4),(3,4)],5) generating graphics... => 4
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 3
([(1,4),(2,3)],5) generating graphics... => 4
([(1,4),(2,3),(3,4)],5) generating graphics... => 3
([(0,1),(2,4),(3,4)],5) generating graphics... => 5
([(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 4
([(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 4
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 5
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 4
([(0,1),(2,3),(2,4),(3,4)],5) generating graphics... => 6
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 5
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 5
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) generating graphics... => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([],6) generating graphics... => 4
([(4,5)],6) generating graphics... => 4
([(3,5),(4,5)],6) generating graphics... => 4
([(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(2,5),(3,4)],6) generating graphics... => 4
([(2,5),(3,4),(4,5)],6) generating graphics... => 3
([(1,2),(3,5),(4,5)],6) generating graphics... => 5
([(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 4
([(0,1),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,4),(3,4)],6) generating graphics... => 5
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 5
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 4
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(2,3)],6) generating graphics... => 4
([(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 4
([(0,1),(2,5),(3,4),(4,5)],6) generating graphics... => 5
([(1,2),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 5
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 4
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 5
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) generating graphics... => 5
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 6
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) generating graphics... => 7
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 6
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 6
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) generating graphics... => 5
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 5
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) generating graphics... => 5
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 4
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(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) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) generating graphics... => 9
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) generating graphics... => 8
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) generating graphics... => 7
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) generating graphics... => 5
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 7
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 6
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(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) generating graphics... => 4
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(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) generating graphics... => 4
([(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) generating graphics... => 4
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(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) generating graphics... => 4
([(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) generating graphics... => 6
([(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) generating graphics... => 5
([(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) generating graphics... => 5
([(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) generating graphics... => 5
click to show generating function       
Description
The disjunction number of a graph.
Let $V_n$ be the power set of $\{1,\dots,n\}$ and let $E_n=\{(a,b)| a,b\in V_n, a\neq b, a\cap b=\emptyset\}$. Then the disjunction number of a graph $G$ is the smallest integer $n$ such that $(V_n, E_n)$ has an induced subgraph isomorphic to $G$.
References
[1] van der Zypen, D. Disjunction number of a graph MathOverflow:331366
Code
def Dominics_graph(n):
    V = map(frozenset, powerset(range(n)))
    return Graph([V, lambda a, b: a != b and a.isdisjoint(b)])

def statistic(G):
    n = 0
    while True:
        H = Dominics_graph(n)
        H.relabel()
        if H.subgraph_search(G, induced=True):
            return n
        n += 1

Created
May 13, 2019 at 08:43 by Martin Rubey
Updated
May 14, 2019 at 12:51 by Martin Rubey