Identifier
Values
['A',1] => ([],1) => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6
['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) => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
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Description
The harmonious chromatic number of a graph.
A harmonious colouring is a proper vertex colouring such that any pair of colours appears at most once on adjacent vertices.
A harmonious colouring is a proper vertex colouring such that any pair of colours appears at most once on adjacent vertices.
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 $\alpha \prec \beta$ 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
complement
Description
The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
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