The Group Structure of Pivot and Loop Complementation on Graphs and Set Systems

@article{Brijder2011TheGS,
  title={The Group Structure of Pivot and Loop Complementation on Graphs and Set Systems},
  author={Robert Brijder and Hendrik Jan Hoogeboom},
  journal={Eur. J. Comb.},
  year={2011},
  volume={32},
  pages={1353-1367}
}
We study the interplay between principal pivot transform (pivot) and loop complementation for graphs. This is done by generalizing loop complementation (in addition to pivot) to set systems. We show that the operations together, when restricted to single vertices, form the permutation group S3. This leads, e.g., to a normal form for sequences of pivots and loop complementation on graphs. The results have consequences for the operations of local complementation and edge complementation on simple… CONTINUE READING