Processing math: 100%

Identifier
Values
['A',1] => ([],1) => ([],1) => [1] => 1
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => [2,1] => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => [2,1,1] => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => [2,1,1,1,1] => 2
['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) => [5,1] => 8
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Description
The number of graphs with given frequency partition.
The frequency partition of a graph on n vertices is the partition obtained from its degree sequence by recording and sorting the frequencies of the numbers that occur.
For example, the complete graph on n vertices has frequency partition (n). The path on n vertices has frequency partition (n−2,2), because its degree sequence is (2,…,2,1,1). The star graph on n vertices has frequency partition is (n−1,1), because its degree sequence is (n−1,1,…,1).
There are two graphs having frequency partition (2,1): the path and an edge together with an isolated vertex.
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the 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.