Values
([],1) => ([],1) => 0
([],2) => ([],2) => 0
([(0,1)],2) => ([(0,1)],2) => 2
([],3) => ([],3) => 0
([(1,2)],3) => ([(1,2)],3) => 2
([],4) => ([],4) => 0
([(2,3)],4) => ([(2,3)],4) => 2
([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => 4
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
([],5) => ([],5) => 0
([(3,4)],5) => ([(3,4)],5) => 2
([(0,1),(0,2),(0,3),(0,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(1,2),(1,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
([(0,4),(4,1),(4,2),(4,3)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,4),(1,4),(4,2),(4,3)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,4),(1,4),(2,4),(4,3)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 4
([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
([],6) => ([],6) => 0
([(4,5)],6) => ([(4,5)],6) => 2
([(1,2),(1,3),(1,4),(1,5)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 6
([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
([(1,5),(5,2),(5,3),(5,4)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(1,5),(2,5),(5,3),(5,4)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(1,5),(2,5),(3,5),(5,4)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 4
([(2,4),(2,5),(3,4),(3,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 6
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 6
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 6
([],7) => ([],7) => 0
([(5,6)],7) => ([(5,6)],7) => 2
([(2,3),(2,4),(2,5),(2,6)],7) => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 6
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(3,4),(3,5),(4,6),(5,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
([(2,6),(6,3),(6,4),(6,5)],7) => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
([(2,6),(3,6),(6,4),(6,5)],7) => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
([(2,6),(3,6),(4,6),(6,5)],7) => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
([(2,6),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(0,6),(1,6),(2,3),(6,4),(6,5)],7) => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(1,6),(2,6),(3,4),(4,5),(4,6)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => 4
([(3,5),(3,6),(4,5),(4,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(1,6),(2,3),(2,4),(2,6),(6,5)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8
([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 6
([(1,4),(1,5),(2,3),(2,5),(3,6),(4,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8
([(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8
([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8
([(1,6),(5,3),(5,4),(6,2),(6,5)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(1,6),(2,3),(3,5),(3,6),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(0,5),(1,6),(6,2),(6,3),(6,4)],7) => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 6
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 6
([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(0,6),(1,3),(1,5),(4,2),(5,4),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(0,6),(1,5),(2,3),(2,4),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(0,4),(0,6),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(0,6),(1,4),(1,5),(2,3),(2,5),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 8
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Description
The energy of a graph, if it is integral.
The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3].
The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3].
The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
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Description
Returns the Hasse diagram of the poset as an undirected graph.
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