Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000422
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Mapping
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 0
[1,2] => [2] => ([],2)
 => ([],2)
 => 0
[2,1] => [2] => ([],2)
 => ([],2)
 => 0
[1,2,3] => [3] => ([],3)
 => ([],3)
 => 0
[1,3,2] => [1,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
[2,1,3] => [3] => ([],3)
 => ([],3)
 => 0
[2,3,1] => [3] => ([],3)
 => ([],3)
 => 0
[3,1,2] => [3] => ([],3)
 => ([],3)
 => 0
[1,2,3,4] => [4] => ([],4)
 => ([],4)
 => 0
[1,3,2,4] => [1,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => 2
[1,3,4,2] => [1,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => 2
[1,4,2,3] => [1,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => 2
[2,1,3,4] => [4] => ([],4)
 => ([],4)
 => 0
[2,3,1,4] => [4] => ([],4)
 => ([],4)
 => 0
[2,3,4,1] => [4] => ([],4)
 => ([],4)
 => 0
[2,4,1,3] => [4] => ([],4)
 => ([],4)
 => 0
[3,1,2,4] => [4] => ([],4)
 => ([],4)
 => 0
[3,4,1,2] => [4] => ([],4)
 => ([],4)
 => 0
[4,1,2,3] => [4] => ([],4)
 => ([],4)
 => 0
[4,3,1,2] => [1,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => 2
[1,2,3,4,5] => [5] => ([],5)
 => ([],5)
 => 0
[1,3,2,4,5] => [1,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2
[1,3,4,2,5] => [1,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2
[1,3,4,5,2] => [1,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2
[1,3,5,2,4] => [1,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2
[1,4,2,3,5] => [1,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2
[1,4,5,2,3] => [1,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2
[1,5,2,3,4] => [1,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2
[1,5,4,2,3] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 4
[2,1,3,4,5] => [5] => ([],5)
 => ([],5)
 => 0
[2,3,1,4,5] => [5] => ([],5)
 => ([],5)
 => 0
[2,3,4,1,5] => [5] => ([],5)
 => ([],5)
 => 0
[2,3,4,5,1] => [5] => ([],5)
 => ([],5)
 => 0
[2,3,5,1,4] => [5] => ([],5)
 => ([],5)
 => 0
[2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[2,4,1,3,5] => [5] => ([],5)
 => ([],5)
 => 0
[2,4,5,1,3] => [5] => ([],5)
 => ([],5)
 => 0
[2,4,5,3,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[2,5,1,3,4] => [5] => ([],5)
 => ([],5)
 => 0
[2,5,1,4,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[2,5,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[3,1,2,4,5] => [5] => ([],5)
 => ([],5)
 => 0
[3,2,1,5,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
[3,4,1,2,5] => [5] => ([],5)
 => ([],5)
 => 0
[3,4,5,1,2] => [5] => ([],5)
 => ([],5)
 => 0
[3,4,5,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[3,5,1,2,4] => [5] => ([],5)
 => ([],5)
 => 0
[3,5,1,4,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[3,5,2,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[4,1,2,3,5] => [5] => ([],5)
 => ([],5)
 => 0
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.