Identifier
Values
['A',1] => ([],1) => ([],1) => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => ([(1,2)],3) => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => ([(2,3)],4) => 0
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => ([(4,5)],6) => 0
['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) => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
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
Description
The number of two-component spanning forests of a graph.
A spanning subgraph is a subgraph which contains all vertices of the ambient graph. A forest is a graph which contains no cycles, and has any number of connected components. A two-component spanning forest is a spanning subgraph which contains no cycles and has two connected components.
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
connected complement
Description
The componentwise connected complement of a graph.
For a connected graph $G$, this map returns the complement of $G$ if it is connected, otherwise $G$ itself. If $G$ is not connected, the map is applied to each connected component separately.
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.