Identifier
Values
[[]] => ([(0,1)],2) => ([(1,2)],3) => 0
[[],[]] => ([(0,2),(1,2)],3) => ([(1,3),(2,3)],4) => 0
[[[]]] => ([(0,2),(1,2)],3) => ([(1,3),(2,3)],4) => 0
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(1,4),(2,4),(3,4)],5) => 0
[[[],[]]] => ([(0,3),(1,3),(2,3)],4) => ([(1,4),(2,4),(3,4)],5) => 0
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
vertex addition
Description
Adds a disconnected vertex to a graph.