English

On the linear algebra of local complementation

Combinatorics 2011-06-28 v4

Abstract

We explore the connections between the linear algebra of symmetric matrices over GF(2) and the circuit theory of 4-regular graphs. In particular, we show that the equivalence relation on simple graphs generated by local complementation can also be generated by an operation defined using inverse matrices.

Keywords

Cite

@article{arxiv.1101.1246,
  title  = {On the linear algebra of local complementation},
  author = {Lorenzo Traldi},
  journal= {arXiv preprint arXiv:1101.1246},
  year   = {2011}
}

Comments

22 pages, 5 figures. v2 includes two new results and several minor corrections. v3 includes minor corrections and updated references. v4 has 24 pages and 6 figures; it includes new examples and many modest corrections and revisions. Further revisions may be made before publication in Linear Algebra and its Applications

R2 v1 2026-06-21T17:08:27.677Z