Identifier
Values
[1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => ([(1,2)],3) => 0
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2)],4) => -1
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2)],4) => -1
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2)],4) => -1
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2)],4) => -1
[3,2,1] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => ([(1,2)],3) => 0
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
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.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.