Identifier
Values
['A',1] => ([],1) => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => 2
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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 Kn 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 Kn equals 2n−2. For this reason, we do not define the energy of the empty graph.
Map
incomparability graph
Description
The incomparability graph of a poset.
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.
This is the poset on the set of positive roots of its root system where α≺β if β−α is a simple root.
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