Identifier
Values
00 => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => ([(1,2)],3) => 0
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2)],4) => -1
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2)],4) => -1
11 => ([(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
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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
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
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.