Identifier
Values
['A',1] => ([],1) => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
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Description
The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph.
Let $n(G)$ be the number of vertices of a graph $G$, $m(G)$ be its number of edges and let $\alpha(G)$ be its independence number, St000093The cardinality of a maximal independent set of vertices of a graph.. Turán's theorem is that $m(G) \geq m(T^c(n(G), \alpha(G)))$ where $T^c(n, r)$ is the complement of the Turán graph.
This statistic records the difference.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.