Identifier
Values
([],1) => ([],1) => ([],1) => ([],1) => 0
([],2) => ([],1) => ([],1) => ([],1) => 0
([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([],3) => ([],1) => ([],1) => ([],1) => 0
([(1,2)],3) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,1),(0,2)],3) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,2),(1,2)],3) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([],4) => ([],1) => ([],1) => ([],1) => 0
([(2,3)],4) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,2),(1,3)],4) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,1),(0,2),(0,3)],4) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,3),(2,3)],4) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([],5) => ([],1) => ([],1) => ([],1) => 0
([(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(2,3),(2,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,2),(1,3),(1,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,1),(0,2),(0,3),(0,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,4),(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,4),(1,2),(1,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,3),(0,4),(1,2),(1,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([],6) => ([],1) => ([],1) => ([],1) => 0
([(4,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,2),(1,3),(1,4),(1,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,5),(1,5),(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,5),(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,5),(1,5),(2,3),(2,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,5),(2,3),(2,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,5),(1,2),(1,3),(1,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,4),(1,5),(2,3),(2,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,4),(0,5),(1,2),(1,3)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([],7) => ([],1) => ([],1) => ([],1) => 0
([(5,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(4,5),(4,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(2,3),(2,4),(2,5),(2,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(4,6),(5,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(2,6),(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(2,6),(3,5),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
([(1,6),(2,6),(3,4),(3,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,6),(2,6),(3,5),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
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Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
maximal antichains
Description
The lattice of maximal antichains in a poset.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains can be ordered by setting $A \leq B \Leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow}B$, where $\mathop{\downarrow}A$ is the order ideal generated by $A$.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains can be ordered by setting $A \leq B \Leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow}B$, where $\mathop{\downarrow}A$ is the order ideal generated by $A$.
Map
to poset
Description
Return the poset corresponding to the lattice.
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