- FindStat

edit this statistic or download as text // json

Identifier

St001351: Graphs ⟶ ℤ

Values

([],1) => 0

([],2) => 0

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

([],3) => 0

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

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

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

([],4) => 0

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

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

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

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

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

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

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

([(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) => 0

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

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

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

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

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

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

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

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

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

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

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

([(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) => 6

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

([(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) => 2

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

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

([(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) => 4

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

([(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) => 0

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

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

([(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) => 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) => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 2

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

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

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

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

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

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

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

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

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

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

([(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) => 4

>>> 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

Description

The Albertson index of a graph.
This is $\sum_{\{u,v\}\in E} |d(u)-d(v)|$, where $E$ is the set of edges and $d_v$ is the degree of vertex $v$, see [1].
In particular, this statistic vanishes on graphs whose components are all regular, see [2].

References

[1] Albertson, M. O. The irregularity of a graph MathSciNet:1470801
[2] Number of simple graphs on n vertices with each component regular. OEIS:A165647

Code

def statistic(G):
    return sum(abs(G.degree(u)-G.degree(v)) for u, v in G.edges(labels=False))

Created

Feb 06, 2019 at 06:09 by Martin Rubey

Updated

Dec 23, 2020 at 11:50 by Martin Rubey