- FindStat

edit this statistic or download as text // json

Identifier

St001522: Graphs ⟶ ℤ

Values

([],1) => 0

([],2) => 0

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

([],3) => 0

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

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

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

([],4) => 0

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

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

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

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

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

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

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

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

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

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

([],5) => 0

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

([(2,4),(3,4)],5) => 10

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

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

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

([(1,4),(2,3),(3,4)],5) => 10

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

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

([(0,4),(1,4),(2,3),(3,4)],5) => 10

([(1,4),(2,3),(2,4),(3,4)],5) => 14

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 14

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

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

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 14

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

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 14

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

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

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

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

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

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

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

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

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 10

([(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) => 12

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10

([(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) => 6

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

([],6) => 0

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

([(3,5),(4,5)],6) => 14

([(2,5),(3,5),(4,5)],6) => 18

([(1,5),(2,5),(3,5),(4,5)],6) => 20

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 20

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

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

([(1,2),(3,5),(4,5)],6) => 10

([(3,4),(3,5),(4,5)],6) => 18

([(1,5),(2,5),(3,4),(4,5)],6) => 18

([(0,1),(2,5),(3,5),(4,5)],6) => 10

([(2,5),(3,4),(3,5),(4,5)],6) => 22

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 18

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

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

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

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

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 18

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 14

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

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 22

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 16

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 18

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 26

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 22

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 26

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 18

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 16

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 18

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 26

([(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) => 26

([(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) => 24

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

([(1,5),(2,4),(3,4),(3,5)],6) => 14

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

([(1,2),(3,4),(3,5),(4,5)],6) => 14

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 14

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 18

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 14

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 18

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 20

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 20

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 10

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 16

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 18

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 10

>>> Load all 1200 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

$F_{1} = 1$

$F_{2} = 2$

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

$F_{4} = 4 + 3\ q^{4} + 4\ q^{6}$

$F_{5} = 3 + 4\ q^{4} + 6\ q^{6} + 4\ q^{8} + 6\ q^{10} + 7\ q^{12} + 4\ q^{14}$

$F_{6} = 8 + 22\ q^{8} + 14\ q^{10} + 20\ q^{14} + 20\ q^{16} + 32\ q^{18} + 8\ q^{20} + 12\ q^{22} + 12\ q^{24} + 8\ q^{26}$

Description

The total irregularity of a graph.
This is the sum of the absolute values of the degree differences of all pairs of vertices:

$\frac{1}{2}\sum_{u,v} |d_u-d_v|$

References

[1] Abdo, H., Brandt, S., Dimitrov, D. The total irregularity of a graph MathSciNet:3214266

Code

def statistic(G):
    return sum(abs(G.degree(u)-G.degree(v)) for u in range(G.num_verts()) for v in range(u))

Created

Feb 29, 2020 at 17:21 by Martin Rubey

Updated

Feb 29, 2020 at 17:21 by Martin Rubey