On the linear algebra of local complementation
arXiv:1101.1246
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.
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