Values
=>
Cc0020;cc-rep
([],1)=>0
([],2)=>0
([(0,1)],2)=>2
([],3)=>0
([(1,2)],3)=>2
([(0,1),(0,2),(1,2)],3)=>4
([],4)=>0
([(2,3)],4)=>2
([(0,3),(1,2)],4)=>4
([(1,2),(1,3),(2,3)],4)=>4
([(0,2),(0,3),(1,2),(1,3)],4)=>4
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>6
([],5)=>0
([(3,4)],5)=>2
([(0,4),(1,4),(2,4),(3,4)],5)=>4
([(1,4),(2,3)],5)=>4
([(2,3),(2,4),(3,4)],5)=>4
([(1,3),(1,4),(2,3),(2,4)],5)=>4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6
([(0,1),(2,3),(2,4),(3,4)],5)=>6
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>8
([],6)=>0
([(4,5)],6)=>2
([(1,5),(2,5),(3,5),(4,5)],6)=>4
([(2,5),(3,4)],6)=>4
([(3,4),(3,5),(4,5)],6)=>4
([(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>6
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,5),(1,4),(2,3)],6)=>6
([(1,2),(3,4),(3,5),(4,5)],6)=>6
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>6
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>6
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>8
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>8
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>8
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([],7)=>0
([(5,6)],7)=>2
([(2,6),(3,6),(4,6),(5,6)],7)=>4
([(3,6),(4,5)],7)=>4
([(4,5),(4,6),(5,6)],7)=>4
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>6
([(3,5),(3,6),(4,5),(4,6)],7)=>4
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>6
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6
([(1,6),(2,5),(3,4)],7)=>6
([(2,3),(4,5),(4,6),(5,6)],7)=>6
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>6
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>8
([(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)=>6
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)=>8
([(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),(3,6),(4,6),(5,6)],7)=>10
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>8
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>8
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>8
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)=>8
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>8
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>8
([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>10
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>10
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>10
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>10
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>10
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>12
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>10
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>12
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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.
References
[1] wikipedia:Graph_energy
[2] Bapat, R. B., Pati, S. Energy of a graph is never an odd integer MathSciNet:2250987
[3] Pirzada, S., Gutman, I. Energy of a graph is never the square root of an odd integer MathSciNet:2396734
[2] Bapat, R. B., Pati, S. Energy of a graph is never an odd integer MathSciNet:2250987
[3] Pirzada, S., Gutman, I. Energy of a graph is never the square root of an odd integer MathSciNet:2396734
Code
def statistic(G):
return sum(abs(c) for c in G.spectrum())
Created
Feb 26, 2016 at 11:47 by Martin Rubey
Updated
Feb 26, 2016 at 12:08 by Martin Rubey
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