Identifier
Values
([],1) => ([],1) => ([],1) => 0
([],2) => ([],2) => ([],2) => 0
([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 2
([],3) => ([],3) => ([],3) => 0
([(1,2)],3) => ([(1,2)],3) => ([(1,2)],3) => 2
([],4) => ([],4) => ([],4) => 0
([(2,3)],4) => ([(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) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6
([(0,3),(1,2)],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) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6
([],5) => ([],5) => ([],5) => 0
([(3,4)],5) => ([(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) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
([(1,2),(1,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
([(0,4),(4,1),(4,2),(4,3)],5) => ([(0,4),(1,4),(2,4),(3,4)],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) => ([(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) => ([(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) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
([(1,4),(2,3)],5) => ([(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) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
([],6) => ([],6) => ([],6) => 0
([(4,5)],6) => ([(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) => ([(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) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(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
([(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) => ([(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
([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(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
([(1,5),(5,2),(5,3),(5,4)],6) => ([(1,5),(2,5),(3,5),(4,5)],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) => ([(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) => ([(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) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],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) => ([(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) => ([(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) => ([(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) => ([(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) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
([(2,5),(3,4)],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) => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],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) => ([(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) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(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
([(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) => ([(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
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(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
([(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) => ([(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) => ([(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) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(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
([(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) => ([(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) => ([(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) => ([(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) => ([(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) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(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
([(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) => ([(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) => ([],7) => ([],7) => 0
([(5,6)],7) => ([(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) => ([(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) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => ([(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
([(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) => ([(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
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([(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) => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => ([(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
([(2,6),(6,3),(6,4),(6,5)],7) => ([(2,6),(3,6),(4,6),(5,6)],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) => ([(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) => ([(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) => ([(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) => ([(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) => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
([(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) => ([(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) => ([(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) => ([(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) => ([(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) => ([(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) => ([(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) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(3,6),(4,5)],7) => ([(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) => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
([(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) => ([(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) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
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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.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
Ore closure
Description
The Ore closure of a graph.
The Ore closure of a connected graph $G$ has the same vertices as $G$, and the smallest set of edges containing the edges of $G$ such that for any two vertices $u$ and $v$ whose sum of degrees is at least the number of vertices, then $(u,v)$ is also an edge.
For disconnected graphs, we compute the closure separately for each component.
The Ore closure of a connected graph $G$ has the same vertices as $G$, and the smallest set of edges containing the edges of $G$ such that for any two vertices $u$ and $v$ whose sum of degrees is at least the number of vertices, then $(u,v)$ is also an edge.
For disconnected graphs, we compute the closure separately for each component.
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