- FindStat

Identifier

Mp00011: Binary trees —to graph⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000259: Graphs ⟶ ℤ

Values

[.,.] => ([],1) => ([],1) => ([],1) => 0

[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[[[[[.,.],.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,.]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,.]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,.]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,.],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[.,.]]],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[.,.],.]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[.,.],.]],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[.,.]],.],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[.,.],.],.],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[[.,.],.]]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[.,[.,.]],.]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[[.,.],.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[[.,.],.]],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[.,[[[[.,.],.],.],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[.,[[[.,.],.],.]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[.,[[.,.],.]],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[[.,[.,.]],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[[[[[[.,.],.],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3

[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 3

[.,[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[[.,.],[.,.]],.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 3

[.,[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,.],[[.,[.,.]],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,[.,[.,.]]],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,[[.,.],.]],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[.,[.,.]],.],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,[[.,.],[.,.]]],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 3

[.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[.,.],[.,[.,.]]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[.,.],[[.,.],.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[.,[.,.]],[.,.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[[.,.],.],[.,.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[[.,.],[.,.]],.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 3

[.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

[.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3

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$F_{1} = 1$

Description

The diameter of a connected graph.
This is the greatest distance between any pair of vertices.

Map

to graph

Description

Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.

Map

square

Description

The square of a graph.
For a graph

$G$ , the square is the graph on the same set of vertices where two vertices are joined by an edge if there is a path in

$G$ of length at most two between the two.
In other words, a vertex gets joint to its

$2$ -neighbourhood in G.

Map

complement

Description

The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.