- FindStat

edit this statistic or download as text // json

Identifier

St001109: Graphs ⟶ ℤ

Values

([],1) => 1

([],2) => 1

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

([],3) => 1

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

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

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

([],4) => 1

([(2,3)],4) => 8

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

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

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

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

([(1,2),(1,3),(2,3)],4) => 18

([(0,3),(1,2),(1,3),(2,3)],4) => 12

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

([(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) => 24

([],5) => 1

([(3,4)],5) => 16

([(2,4),(3,4)],5) => 8

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

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

([(1,4),(2,3)],5) => 8

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

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

([(2,3),(2,4),(3,4)],5) => 54

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

([(1,4),(2,3),(2,4),(3,4)],5) => 36

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 24

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

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

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 18

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 24

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 12

([(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) => 6

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

([(0,1),(2,3),(2,4),(3,4)],5) => 36

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 24

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 12

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 30

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 18

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

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 12

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 96

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 72

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 48

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 12

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

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 24

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 120

([],6) => 1

([(4,5)],6) => 32

([(3,5),(4,5)],6) => 16

([(2,5),(3,5),(4,5)],6) => 8

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

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

([(2,5),(3,4)],6) => 16

([(2,5),(3,4),(4,5)],6) => 8

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

([(3,4),(3,5),(4,5)],6) => 162

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

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

([(2,5),(3,4),(3,5),(4,5)],6) => 108

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

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 72

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 48

([(2,4),(2,5),(3,4),(3,5)],6) => 8

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

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

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

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 54

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 72

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

([(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) => 36

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 48

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24

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

([(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) => 18

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12

([(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) => 6

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

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

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

([(1,2),(3,4),(3,5),(4,5)],6) => 108

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

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 72

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 72

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 48

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 36

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 24

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 90

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

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 54

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 60

>>> Load all 1220 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The number of proper colourings of a graph with as few colours as possible.
By definition, this is the evaluation of the chromatic polynomial at the first nonnegative integer which is not a zero of the polynomial.

References

[1] wikipedia:Chromatic polynomial

Code

def statistic(G):
    return G.chromatic_polynomial().subs(G.chromatic_number())

Created

Feb 19, 2018 at 08:51 by Martin Rubey

Updated

Oct 17, 2018 at 09:23 by Martin Rubey