Processing math: 100%

Identifier
Values
['A',1] => ([],1) => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 1
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
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searching the database for statistics with the same generating function
Description
The absolute value of the derivative of the chromatic polynomial of the graph at 1.
This is closely related to Crapo's beta invariant, the only difference being the value for the graphs without edges.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let G=(V,E) be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods {Nv|v∈V} of G, and has an edge (Na,Nb) between two vertices if and only if (a,b) is an edge of G. This is well-defined, because if Na=Nc and Nb=Nd, then (a,b)∈E if and only if (c,d)∈E.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
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 α≺β if β−α is a simple root.