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Identifier

St001322: Graphs ⟶ ℤ

Values

([],1) => 1

([],2) => 2

([(0,1)],2) => 1

([],3) => 3

([(1,2)],3) => 2

([(0,2),(1,2)],3) => 1

([(0,1),(0,2),(1,2)],3) => 1

([],4) => 4

([(2,3)],4) => 3

([(1,3),(2,3)],4) => 2

([(0,3),(1,3),(2,3)],4) => 1

([(0,3),(1,2)],4) => 2

([(0,3),(1,2),(2,3)],4) => 2

([(1,2),(1,3),(2,3)],4) => 2

([(0,3),(1,2),(1,3),(2,3)],4) => 1

([(0,2),(0,3),(1,2),(1,3)],4) => 2

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([],5) => 5

([(3,4)],5) => 4

([(2,4),(3,4)],5) => 3

([(1,4),(2,4),(3,4)],5) => 2

([(0,4),(1,4),(2,4),(3,4)],5) => 1

([(1,4),(2,3)],5) => 3

([(1,4),(2,3),(3,4)],5) => 3

([(0,1),(2,4),(3,4)],5) => 2

([(2,3),(2,4),(3,4)],5) => 3

([(0,4),(1,4),(2,3),(3,4)],5) => 2

([(1,4),(2,3),(2,4),(3,4)],5) => 2

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(1,3),(1,4),(2,3),(2,4)],5) => 3

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 2

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,4),(1,3),(2,3),(2,4)],5) => 2

([(0,1),(2,3),(2,4),(3,4)],5) => 2

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 2

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 1

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 2

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 2

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 2

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 1

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1

([],6) => 6

([(4,5)],6) => 5

([(3,5),(4,5)],6) => 4

([(2,5),(3,5),(4,5)],6) => 3

([(1,5),(2,5),(3,5),(4,5)],6) => 2

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

([(2,5),(3,4)],6) => 4

([(2,5),(3,4),(4,5)],6) => 4

([(1,2),(3,5),(4,5)],6) => 3

([(3,4),(3,5),(4,5)],6) => 4

([(1,5),(2,5),(3,4),(4,5)],6) => 3

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

([(2,5),(3,4),(3,5),(4,5)],6) => 3

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

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2

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

([(2,4),(2,5),(3,4),(3,5)],6) => 4

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

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3

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

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 3

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

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

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

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

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

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3

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

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

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

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

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

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

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

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

([(1,5),(2,4),(3,4),(3,5)],6) => 3

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

([(1,2),(3,4),(3,5),(4,5)],6) => 3

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

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3

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

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

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 2

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

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 3

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

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 3

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

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = 2\ q + q^{2} + q^{3}$

$F_{4} = 4\ q + 5\ q^{2} + q^{3} + q^{4}$

$F_{5} = 11\ q + 16\ q^{2} + 5\ q^{3} + q^{4} + q^{5}$

$F_{6} = 34\ q + 90\ q^{2} + 25\ q^{3} + 5\ q^{4} + q^{5} + q^{6}$

Description

The size of a minimal independent dominating set in a graph.

Code

def statistic(G):
    return G.dominating_set(independent=True, value_only=True)

Created

Dec 14, 2018 at 13:38 by Martin Rubey

Updated

Dec 28, 2018 at 15:49 by Martin Rubey