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.
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