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Identifier
Values
['A',1] => ([],1) => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(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) => 2
['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) => 3
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The monophonic hull number of a graph.
The monophonic hull of a set of vertices M of a graph G is the set of vertices that lie on at least one induced path between vertices in M. The monophonic hull number is the size of the smallest set M such that the monophonic hull of M is all of G.
For example, the monophonic hull number of a graph G with n vertices is n if and only if G is a disjoint union of complete graphs.
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 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.