Identifier
Values
[[]] => ([(0,1)],2) => ([],2) => 0
[[],[]] => ([(0,2),(1,2)],3) => ([],2) => 0
[[[]]] => ([(0,2),(1,2)],3) => ([],2) => 0
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([],2) => 0
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2)],4) => 2
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2)],4) => 2
[[[],[]]] => ([(0,3),(1,3),(2,3)],4) => ([],2) => 0
[[[[]]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2)],4) => 2
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([],2) => 0
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 2
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 2
[[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 2
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([],2) => 0
[[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 2
[[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 2
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => 0
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => 0
[[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 2
[[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 2
[[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => 0
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 2
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 2
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => 0
[[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[],[],[[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[],[],[[[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[],[[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[],[[[]]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 2
[[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[[],[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[[[]]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
[[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 2
[[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 2
[[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 2
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Description
The number of cover relations in a poset.
Equivalently, this is also the number of edges in the Hasse diagram [1].
Equivalently, this is also the number of edges in the Hasse diagram [1].
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
weak duplicate order
Description
The weak duplicate order of the de-duplicate of a graph.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.
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