Identifier
Values
[(1,2),(3,4)] => [(1,4),(2,3)] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[(1,3),(2,4)] => [(1,3),(2,4)] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 3
[(1,2),(3,4),(5,6)] => [(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[(1,3),(2,4),(5,6)] => [(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[(1,4),(2,3),(5,6)] => [(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[(1,5),(2,3),(4,6)] => [(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[(1,2),(3,5),(4,6)] => [(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[(1,4),(2,6),(3,5)] => [(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 2
[(1,5),(2,6),(3,4)] => [(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
search for individual values
searching the database for the individual values of this statistic
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Map
rotation
Description
The rotation of a perfect matching.
This returns the perfect matching obtained by relabelling $i$ to $i+1$ cyclically.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.