Identifier
Values
['A',1] => ([],1) => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => 4
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 9
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Description
Half the total irregularity of a graph.
This is half the sum of the absolute values of the degree differences of all pairs of vertices:
$$ \frac{1}{4}\sum_{u,v} |d_u-d_v| $$
It is easy to show by induction on the number of edges that this is an integer.
This is half the sum of the absolute values of the degree differences of all pairs of vertices:
$$ \frac{1}{4}\sum_{u,v} |d_u-d_v| $$
It is easy to show by induction on the number of edges that this is an integer.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
Map
incomparability graph
Description
The incomparability graph of a poset.
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