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Statistic identifier: St001391

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Collection: Graphs

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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 $G$.

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References: [1]   van der Zypen, D. Disjunction number of a graph [[MathOverflow:331366]]

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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


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Statistic values:

([],1)                                                                                          => 0
([],2)                                                                                          => 2
([(0,1)],2)                                                                                     => 1
([],3)                                                                                          => 3
([(1,2)],3)                                                                                     => 2
([(0,2),(1,2)],3)                                                                               => 2
([(0,1),(0,2),(1,2)],3)                                                                         => 2
([],4)                                                                                          => 3
([(2,3)],4)                                                                                     => 3
([(1,3),(2,3)],4)                                                                               => 3
([(0,3),(1,3),(2,3)],4)                                                                         => 3
([(0,3),(1,2)],4)                                                                               => 4
([(0,3),(1,2),(2,3)],4)                                                                         => 3
([(1,2),(1,3),(2,3)],4)                                                                         => 3
([(0,3),(1,2),(1,3),(2,3)],4)                                                                   => 2
([(0,2),(0,3),(1,2),(1,3)],4)                                                                   => 4
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)                                                             => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)                                                       => 3
([],5)                                                                                          => 4
([(3,4)],5)                                                                                     => 3
([(2,4),(3,4)],5)                                                                               => 3
([(1,4),(2,4),(3,4)],5)                                                                         => 4
([(0,4),(1,4),(2,4),(3,4)],5)                                                                   => 3
([(1,4),(2,3)],5)                                                                               => 4
([(1,4),(2,3),(3,4)],5)                                                                         => 3
([(0,1),(2,4),(3,4)],5)                                                                         => 5
([(2,3),(2,4),(3,4)],5)                                                                         => 4
([(0,4),(1,4),(2,3),(3,4)],5)                                                                   => 4
([(1,4),(2,3),(2,4),(3,4)],5)                                                                   => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)                                                             => 3
([(1,3),(1,4),(2,3),(2,4)],5)                                                                   => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)                                                             => 4
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                             => 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)                                                             => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                       => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)                                                       => 5
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                 => 4
([(0,4),(1,3),(2,3),(2,4)],5)                                                                   => 4
([(0,1),(2,3),(2,4),(3,4)],5)                                                                   => 6
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)                                                             => 5
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)                                                       => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)                                                             => 5
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)                                                       => 4
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)                                                 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)                                                       => 4
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                       => 4
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                                 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                           => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)                                                 => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)                                           => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                                     => 4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)                               => 4
([],6)                                                                                          => 4
([(4,5)],6)                                                                                     => 4
([(3,5),(4,5)],6)                                                                               => 4
([(2,5),(3,5),(4,5)],6)                                                                         => 4
([(1,5),(2,5),(3,5),(4,5)],6)                                                                   => 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)                                                             => 4
([(2,5),(3,4)],6)                                                                               => 4
([(2,5),(3,4),(4,5)],6)                                                                         => 3
([(1,2),(3,5),(4,5)],6)                                                                         => 5
([(3,4),(3,5),(4,5)],6)                                                                         => 4
([(1,5),(2,5),(3,4),(4,5)],6)                                                                   => 4
([(0,1),(2,5),(3,5),(4,5)],6)                                                                   => 5
([(2,5),(3,4),(3,5),(4,5)],6)                                                                   => 4
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)                                                             => 4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)                                                             => 4
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)                                                       => 3
([(2,4),(2,5),(3,4),(3,5)],6)                                                                   => 4
([(0,5),(1,5),(2,4),(3,4)],6)                                                                   => 5
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                                             => 4
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)                                                             => 5
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                             => 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                             => 3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)                                                             => 4
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                                       => 4
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => 4
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                       => 4
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                                       => 5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)                                                       => 5
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                                 => 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 4
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                           => 5
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 4
([(0,5),(1,4),(2,3)],6)                                                                         => 4
([(1,5),(2,4),(3,4),(3,5)],6)                                                                   => 4
([(0,1),(2,5),(3,4),(4,5)],6)                                                                   => 5
([(1,2),(3,4),(3,5),(4,5)],6)                                                                   => 6
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)                                                             => 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)                                                             => 5
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)                                                             => 6
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                       => 5
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                       => 5
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                                 => 4
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)                                                             => 5
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                                       => 4
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                       => 4
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)                                                       => 5
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                       => 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)                                                       => 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                 => 4
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 4
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                           => 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)                                                             => 5
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)                                                             => 6
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)                                                             => 7
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)                                                       => 5
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)                                                       => 6
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)                                                       => 5
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => 7
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)                                                       => 6
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)                                                 => 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)                                                 => 6
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 5
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 5
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                       => 5
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                                 => 5
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 4
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)                                                 => 6
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)                                           => 5
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 5
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                           => 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                     => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                           => 4
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 4
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                     => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                                 => 5
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                 => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                           => 4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                           => 5
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                     => 4
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)                                                       => 5
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)                                                 => 4
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)                                                 => 4
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)                                                 => 6
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                                 => 5
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)                                                 => 5
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 5
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                           => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                           => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                                     => 4
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)                                           => 5
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                           => 6
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                     => 5
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 4
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 5
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 5
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)                                     => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                     => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                         => 4
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                                     => 6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 5
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                               => 5
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)                         => 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)                   => 5
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)                                                       => 9
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)                                                 => 6
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)                                                 => 8
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                                 => 8
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                                           => 7
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                           => 7
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 6
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)                                           => 7
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)                                     => 6
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 6
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 6
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                                     => 6
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                               => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                         => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)                                           => 5
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                                           => 7
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                                     => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)                               => 5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)                                     => 6
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                               => 5
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                         => 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)                   => 4
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)                               => 5
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                         => 4
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 5
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                               => 5
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                         => 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)                   => 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)             => 4
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                         => 5
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)                         => 5
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)                         => 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)                   => 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)                   => 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)             => 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)       => 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) => 5

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Created: May 13, 2019 at 08:43 by Martin Rubey

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Last Updated: May 14, 2019 at 12:51 by Martin Rubey