TOPICS
Search

Paired Orbital

The paired orbital of an orbital Delta for a permutation group acting on a finite set Omega is

Delta^T={(y,x):(x,y) in Delta}.

It is obtained by reversing the coordinates of every ordered pair in Delta. The orbital Delta is self-paired exactly when Delta=Delta^T. If Delta is the arc set of an orbital digraph, its paired orbital is the arc set obtained by reversing every arc.

See also

Finite Set, Group Orbit, Orbital, Orbital Digraph, Orbital Graph, Permutation Group, Self-Paired Orbital

Explore with Wolfram|Alpha

References

Lauri, J. and Scapellato, R. "Orbital Graphs and Strongly Regular Graphs." Ch. 4 in Topics in Graph Automorphisms and Reconstruction, 2nd ed. Cambridge, England: Cambridge University Press, pp. 64-78, 2016.

Cite this as:

Weisstein, Eric W. "Paired Orbital." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PairedOrbital.html

Subject classifications