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Orbital Digraph


An orbital digraph for a permutation group Gamma acting on a finite set Omega is the directed graph with vertex set Omega and arc set equal to an orbital of Gamma. Reversing every arc gives the orbital digraph of the paired orbital.

If the orbital is self-paired, its opposite arcs can be identified to give an undirected orbital graph.


See also

Directed Graph, Finite Set, Orbital, Orbital Graph, Paired Orbital, Permutation Group, Self-Paired Orbital

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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. "Orbital Digraph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OrbitalDigraph.html

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